WBBSE Solutions For Class 9 Physical Science Chapter 1 Measurement Topic C Measurement Of Different Physical Quantities And Errors In Measurement

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Synopsis

  1. Scale is used for measurement of length.
  2. The smallest scale division is usually 1 mm or 0.1 cm.
  3. While taking the readings of the two sides during measurements of length by an ordinary scale, it is essential to look perpendicularly at the point of reading other wise the reading becomes erroneous, this error, which gives different readings due to different positions of eyes is called parallax error.
  4. Common balance is used for the measurement of the mass of an object.
  5. In a weight box weights are in the ratio 5 : 2: 2: 1.
  6. Sensitivity of a common balance is directly proportional to its capacity of measuring the slightest difference in the mass of an object.
  7. Watch is used for measurement of time.

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Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Short And Long Answer Type Questions

Question 1. Which instrument is used for the measurement of length? Describe this instrument in brief.

Answer: A scale is used for the measurement of length is to be placed on a straight line in such a way.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Measuremnt Of Lenght Scale

The scale is generally made up of thin wood, plastic sheet, aluminium or steel. Its length could be 30 cm, 50 cm or 1 m.On the one side of the scale, the centimetre unit is graduated (marked) and on the other side, the unit inch is marked.

1 centimetre is divided in 10 equal parts, every smallest length being 1 millimetre. One inch is divided into 8 or 16 equal parts. In a metre scale, only millimetre and centimetre markings are present whereas in a foot scale, markings are in inch or its smaller parts.

Question 2. How would you measure the length of a straight line by an ordinary scale?

Answer: Suppose the length of a straight line AB is to be measured by an ordinary scale.

The scale is to be placed on the staright line im such a way that the straight line is along the length of the scale and the graduations of the scale are coincidental to the straight line.

Side A of the line is set to coincide with a fixed marking of the scale.

In this case, it is prudent if side A coincides with a fixed cm. Now looking perpendicularly, reading of the side B is taken. The difference of the two readings gives the length of AB.

Length of line AB = reading of side B – reading of side A = 4.2 cm – 1 cm = 3.2 cm

Question 3. What is meant by parallax error?

Answer:

Parallax Error

While taking the readings of the two sides during measurement of length of a line by an ordinary scale, it is essential to look perpendicularly at the points of the reading.

Otherwise, the reading becomes erroneous. This error, which gives different readings due to different positions of the eyes, is called parallax error.

D is the correct position of the eye.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement

Question 4. How do you measure the thickness of a page of a book with the help of an ordinary scale?

Answer: It is not possible to measure directly a thickness of less than 1 mm by an ordinary scale.

As the thickness of a page is generally less than 1 mm, the thickness of a page is measured indirectly by an ordinary scale.

Suppose there are n number of pages in a book.

By compressing only the pages (excluding the covers) such that the thickness of layers of air between the pages is excluded, the thickness of the book is measured several times. The mean of the readings is, say, b.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement

Then, the thickness of each page is \(\frac{b}{n}\).

Question 5. How do you measure the length of a curved line with the help of a thread and an ordinary scale?

Answer: Measurement of the length of a curved line with the help of a thread and a scale:

A long thread is taken and an ink mark is made at one end (A) of the thread.

Marked end of the thread is placed at one end point of the curved line and the thread is positioned along the curve till it reaches the other end point.

Another ink mark is made on the thread at position B.

Now, this thread is stretched over a scale and the length between the two marks on the thread is measured. This gives the length of the curved line by the thread and scale method.

 

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement (2)

Question 6. How do you measure the diameter of a wire with the help of an ordinary scale?

Answer: It is not possible to directly measure a length less than 1 mm by scale. As the diameter of a thin wire is less than 1 mm, it is measured indirectly.

The wire is wound several times on a cylinder of small radius so that there is no gap between the rounds. Now with the help of a scale, total length of the wounds on the cylinder is measured.

Several measurements are made to take an average measure. Suppose the mean length of the wire is b. If the number of coils made is n, then diameter of wire is \(\frac{b}{n}\).

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Diameter Of A Wire

Question 7. Why is an ordinary scale made up of wood instead of metal?

Answer: Metal is a good conductor of heat. If the temperature of a metal scale is increased or decreased, its length increases or decreases.

As a result, the length between the two markings changes. Thus, a correct reading is obtained only at the temperature at which the scale was marked. If temperature increases, the correct reading is greater than the reading shown on the scale and if temperature decreases, the correct reading is smaller.

Wood is a bad conductor of heat. So, the increase or decrease of the length of wood with changing temperature is ignored. As a result, the reading shown in the scale may be assumed to be correct. Hence, an ordinary scale is made of wood instead of metal.

Question 8. Which instrument is used for the measurement of time? Describe a pendulum clock.

Answer: A clock is used for the measurement of time.

In a pendulum clock, a metal bob is attached to a metallic rod at one end and the other end is tied firmly with a fixed support and is suspended.

This is a pendulum. The length from the point of suspension to the centre of gravity of the bob is known as the working length. The pendulum oscillates in a periodic motion.

There are two hands in the clock, the bigger one indicates minutes and the smaller one indicates hours. The clock works with the help of a spring which stores potential energy when it is wound.

This stored potential energy is the source of energy of a pendulum clock and is converted into kinetic energy. The clock needs to be wound at a regular interval as the clock stops working when the stored potential energy is exhausted.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Pendulum Clock

Question 9. What type of watch is used in swimming and running competitions? What is the problem of using an ordinary clock in these cases?

Answer: Stopwatch is used in swimming and running competitions.

The ordinary clock cannot be started and stopped at will. But the stopwatch may be started and stopped according to our convenience.

Further, one can measure a minimum amount of one second by an ordinary clock whereas with the help of a modern digital stopwatch, a time interval of one-tenth of a second can be measured accurately.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Stop Watch

Question 10. Mention different types of clocks.

Answer: We measure time with the help of clocks. The oldest clock is sundial. With the progress of science and technology, different types of clocks have been invented over the time.

Example: Pendulum clock, table clock, wrist watch, electronic digital watch, chronometer, caesium atomic clock etc.

Question 11. What is the inconvenience of expressing your age in seconds?

Answer: Let us suppose that the age of a person is 14 years. If this is converted to seconds, it becomes 14 x 365 x 86400 s = 441504000s.

Hence, if age is expressed in seconds, the number becomes enormous and is inconvenient to handle. For this reason, convenient units like year, month, day are used to express the age of a person.

Question 12. What is a metronome?

Answer: A metronome (electronic metronome) is a modern watch which measures time very accurately. This watch is used during the launching of artificial satellites.

Question 13. Which instrument is used for measurement of the mass of a body? Elaborate the principle used in the measurement of mass by this instrument.

Answer: Common balance is used for measurement of the mass of a body.

While measuring the mass of a body by a common balance, the body is kept in the left pan while some known standard weights are put in the right pan.

When the balance beam comes to a horizontal position, weight of the body in the left pan becomes equal to the standard weight placed in the right pan. This is the principle of measurement of mass.

Question 14. What do you mean by the sensitivity of a common balance? Write down the conditions for a common balance to be sensitive.

Answer: The sensitivity of a common balance is directly proportional to its capacity of measuring the slightest difference in the mass of a body.

The conditions for a common balance to be sensitive are:

  1. The arms should be long.
  2. The balance beam should be light.
  3. The pointer should be long.
  4. The centre of gravity of the common balance should be situated very near to the fulcrum.

Question 15. Explain whether the mass of a body or Its weight is measured by a common balance.

Answer: The mass of a body and not its weight is measured by a common balance.

While measuring the mass of a body by a common balance, it is placed in the left pan of the common balance and some standard weights are placed in the right pan.

O is the fulcrum of the balance and A, B are the left and right ends of the common balance, respectively.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Measured By A Common Balance

if the acceleration due to gravity of the place is g, then in a horizontal state of the common balance, mass of the body x g x AO

= mass of the standard weights x g x OB or, mass of the body

= mass of the standard weights [AO = OB]

Question 16. Why are the masses of the standard weights in a weight box kept in the ratio of 5:2:2:17.

Answer: The masses of the standard weights in a weight box are kept in the ratio of 5:2:2:1 so that any mass between 10 mg and 211.11 g can be measured using them.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Weight Of The Box

Question 17. What are the qualities of a good common balance?

Answer: Qualities of a good common balance are:

  1. The common balance should be sensitive, that is, it should be able to measure the slightest difference in the mass of a body.
  2. The common balance must be strong.
  3. The common balance should be accurate, i.e., equal amount of masses put in the two pans should keep it horizontal.
  4. The common balance should be stable, i.e., its oscillation should be short-lived.
  5. The lengths of the arms and the masses of the two pans should be equal.

Question 18. Why is a sensitive common balance not stable?

Answer: A common balance is considerably sensitive if the centre of gravity of the common balance is situated very near to the fulcrum. Again, the balance is stable if the centre of gravity is well below the fulcrum.

Now, it is not possible to have two opposite conditions in the same common balance simultaneously. This is the reason why a very sensitive common balance is not stable.

Question 19. The lengths of the two arms of a common balance are equal, but the masses of the two scale pans are different. How do you determine the correct mass of a body?

Answer: Let the masses of the left and the right hand sides of the common balance be M1 and M2 respectively and the actual mass of the body is m.

If a mass m1 is put in the right pan by keeping the body in the left pan, the balance becomes horizontal.

∴ M1 + m = M2 + m1…(1)

Again, keeping the body in the right pan, putting a mass m2 in the left pan makes the balance horizontal.

∴ M1 + m2 = M2 + m……(2)

By subtracting equation (2) from (1), we get

m1 – m2 = m1 – m

or, 2m = m1 + m2 or, \(m=\frac{m_1+m_2}{2}\)

Question 20. The lengths of the two arms of a common balance are unequal but the masses of the two scale pans are equal. How would you measure the correct mass of a body?

Answer: Suppose the lengths of the left and the right sides of the common balance are given by x and taken as m.

The lengths of the arms and the masses of the balance becomes horizontal when by keeping two pans should be equal. the body in the left pan, a mass m1 is put in the right pan.

If the acceleration due to gravity at that place is given by g, then mxg = m1yg…(1)

Again, the balance becomes horizontal when by keeping the body in the right pan, a mass m2 is put in the left pan.

∴ m2xg = m1yg…….(2)

By adding equations (1) and (2), we get

\(\frac{m \times g}{m_2 \times g}=\frac{m_1 y g}{m y g} \text { or, } \frac{m}{m_2}=\frac{m_1}{m}\)

or, \(m^2=m_1 m_2 \quad or, m=\sqrt{m_1 m_2}\)

Question 21. What is a measuring cylinder? How do you measure the volume of a liquid with the help of a measuring cylinder? Or, How do you measure the volume of tea in a tea cup?

Answer: A measuring cylinder is a vessel made up of a strong glass closed at one end, with uniform cross section. This is used for the measurement of volume.

It has graduation marks in millilitres (cm3) on its exterior surface, along its length. Each cm3 is further divided into 5 or 10 equal parts.

To measure the volume of a liquid, it is poured inside the measuring cylinder and the reading of its upper surface is taken. While taking a reading, eyes have to be placed in a perpendicular direction to the point of observation.

For those liquids which wet the glass (like water), for which the upper surface is concave inside the cylinder, reading of the lowest portion of the concave surface is to be taken.

For those liquids which do not wet the glass (like mercury) and for which the upper surface is convex inside the cylinder, reading of the highest portion of the convex surface is to be taken.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Measuring Cylinder

Question 22. How do you measure the volume of an irregular solid body with the help of a measuring cylinder?

Answer: To measure the volume of an irregular solid body with the help of a measuring cylinder, a measuring cylinder is taken whose inner volume is 4 to 5 times larger than the volume of the body and the area of its cross-section is such that the body may easily be entered inside the cylinder.

A liquid, in which the body does not dissolve or float or react chemically, is taken in the cylinder up to a certain height. Suppose the volume of the liquid in this condition is V1 cm3.

Now, a wax-coated, thin and strong thread is fastened with the body and the body is slowly immersed completely inside the liquid.

If the volume of the liquid, with the solid inside it is V2 cm3, then the volume of the body (V1 – V2) cm3.

If the volume of the immersed thread is deducted from this reading, the accurate volume of the body can be obtained.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Irregular Solid Body

Question 23. What are the precautionary measures to be taken while measuring the volume of an irregular solid body by a measuring cylinder?

Answer: Required precautionary measures are:

  1. A liquid, which neither dissolves nor reacts chemically with the body, has to be taken inside the measuring cylinder.
  2. The solid body has to be immersed very slowly in the liquid so that no liquid splashes out.
  3. The thread by which the solid body is wound has to be coated with wax so that the thread does not soak water.
  4. Reading has to be taken in such a way that there is no parallax error.
  5. No bubble of the body should stick to the wax is attached to the stone and it is dipped surface of the cylinder inside the liquid.

Question 24. How do you determine the rate of fall of water from a tap with the help of a volume-measuring cylinder and a stopwatch?

Answer: Rate of fall of water from a tap can be determined with the help of a volume-measuring cylinder and a stopwatch. Suppose water is falling from a tap at a uniform rate.

A dry and empty cylinder is held below a running tap and the stopwatch is switched on immediately. After accumulation of some water, the cylinder is removed from under the tap and the stopwatch is stopped simultaneously.

Readings of the measuring cylinder and the stopwatch gives the volume of water collected during a period. Suppose, V1 volume of water is collected during a time t1.

∴ rate of fall of water, \(W_1=\frac{V_1}{t_1}\)

In this way, several readings are to be taken and the mean of these gives the rate of fall of water which is reasonably error-free.

Unit of rate of fall of water is cm3/s if units of volume of water and time are taken as cm3 and second.

Question 25. How do you measure the volume of piece of stone which does not fit into a measuring cylinder?

Answer: A glass cylinder with an attached side pipe and with sufficient cross-sectional area is taken so that the piece of stone may fit into it.

If water is poured continuously in the above cylinder, it flows out by the side pipe at a particular time.

Now, if the pouring of water is stopped, water level stands just beneath the level of the side pipe.

The measuring cylinder is kept just below the side pipe. Now a thin and strong thread coated with wax is attached to the stone and it is dipped slowly into the water of the glass cylinder.

The stone displaces an equal amount of water of its volume which flows out by the side pipe into the measuring cylinder. The volume of water that is stored in the measuring cylinder is the volume of the piece of stone.

If the volume of the submerged thread is deducted from the last reading, the actual volume of the stone can be obtained.

WBBSE Solutions For Class 9 Physical Science Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Volume Of Piece Of Sound

Question 26. How do you measure the density of a solid body with the help of a common balance and a measuring cylinder?

Answer: At first, the mass of the solid body is measured by the common balance. Suppose, m is the mass of the body. Now a measuring cylinder is taken whose area of cross section is sufficient for entry of the solid body inside the cylinder.

A particular liquid, that neither dissolves nor reacts chemically with the solid, is taken in the cylinder. Suppose, V1 is the volume of the liquid in the cylinder.

Now a thin, strong and wax-coated thread is fastened tightly around the body and is slowly dipped into the liquid of the cylinder.

Let the volume of the liquid with the solid be V2.

Hence, the volume of the body V2 – V1. Here, if the volume of the submerged thread is deducted from the reading V2-V1, actual volume of the body is obtained.

∴ Density of the body, \(d=\frac{m}{V_2-V_1}\)

Question 27. How do you measure the density of a liquid with the help of a common balance and a measuring cylinder?

Answer: At first, the mass of the measuring cylinder in a dry condition is measured by a common balance.

Suppose, the mass is m1.

Next the cylinder is nearly half-filled with the liquid whose density is being measured here.

Volume of the liquid is determined from the scale calibrated on the cylinder. Suppose, V is the volume of the liquid. The mass of the cylinder filled with the liquid is then measured by a common balance.

Suppose, m2 is the mass in this case.

∴ Mass of the liquid = m2 -m1

∴ Density of the liquid = \(\frac{m_2-m_1}{V}\)

Question 28. How do you measure the volume of one drop water of a dropper with the help of a volume measuring cylinder?

Answer: 200 to 300 drops of water are dropped in a dry and empty measuring cylinder using the dropper. Volume of this quantity of water is measured.

Let the volume of water be V cm3 and let n drops of water have been dropped.

∴  Volume of 1 drop of water = \(\frac{V}{n} \mathrm{~cm}^3\)

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Very Short Answer Type Questions Choose The Correct Answer

Question 1. Smallest distance that can be measured by an ordinary scale is

  1. 0.1 cm
  2. 0.01 cm
  3. 0.001 cm
  4. 0.2 cm

Answer: 1. 0.1 cm

Question 2. The length which cannot be measured by an ordinary scale is

  1. 4.2 cm
  2. 2.13 cm
  3. 7.7 cm
  4. 9.5 cm

Answer: 2. 2.13 cm

Question 3. Lengths of the two arms of a common balance are equal but the two pans are of different masses. A body is found to be 20 g and 21 g when put in the left pan and the right pan, respectively. The actual mass of the body is

  1. 20.2 g
  2. 20.4 g
  3. 20.5 g
  4. 20.6 g

Answer: 3. 20.5 g

Question 4. In the weight box of a common balance, the weights are taken in the ratio of

  1. 5:3:2:1
  2. 5:4:2:1
  3. 5:2:2:1
  4. 5:3:3:1

Answer: 3. 5:2:2:1

Question 5. The physical quantity which is measured by a common balance is

  1. Volume
  2. Mass
  3. Weight
  4. Force

Answer: 2. Mass

Question 6. Which of the following instruments can be used to measure the volume of a wooden block of irregular shape?

  1. common balance
  2. Measuring cylinder
  3. Metre scale
  4. Stopwatch

Answer: 2. Measuring cylinder

Question 7. Which of the following is not a prerequisite for sensitivity of a common balance?

  1. Beam of the balance should be long
  2. The balance should be light
  3. The pointer should be small in size
  4. The centre of gravity should be very close to the fulcrum

Answer: 3. The pointer should be small in size

Question 8. Which of the following instruments does not function in a place where there is no gravity?

  1. Spring balance
  2. Common balance
  3. Ordinary scale
  4. Both A and R

Answer: 4. Both A and R

Question 9. When mass of a body is measured on the earth surface by a common balance its value becomes m kg. When the measurement is done on the moon’s surface it is m’kg.If gravitational force on the surface of the moon is only 1/6 as the gravitational force on the earth, then

  1. m = m’
  2. m = 1/6m’
  3. m = 6m’
  4. m = m’ = 0

Answer: 1. m = m’

Question 10. Time taken to complete one oscillation by a second pendulum is

  1. 1s
  2. 2s
  3. 3s
  4. 1/2 s

Answer: 2. 2s

Question 11. Which of the following can be used to measure the area of a metallic strip with irregular shape?

  1. Ordinary scale
  2. Common balance
  3. Graph paper
  4. String

Answer: 3. Graph paper

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Answer In Brief

Question 1. What is the use of a chronometer watch?

Answer: A chronometer watch gives the correct time at Greenwich, London and this time has been adopted as a global standard time.

Question 2. Name an instrument by which a length of 0.01 cm can be measured accurately.

Answer: A length of 0.01 cm can be measured accurately by using slide calipers.

Question 3. Name an instrument by which a length of 0.001 cm can be measured accurately.

Answer: A length of 0.001 cm can be measured accurately by using a screw gauge.

Question 4. What is the effective length of a pendulum clock?

Answer: The effective length of a pendulum clock is. measured from the point of suspension to the centre of mass of its bob.

Question 5. What type of energy is stored in the spring of a pendulum clock?

Answer: Potential energy is stored in the spring of a pendulum clock.

Question 6. Which instrument is used to measure the mass of a body?

Answer: Common balance is used to measure the mass of a body.

Question 7. What is the ratio in which the weights are kept in a weight box?

Answer: Weights are kept in the ratio of 5:2:2:1 in a weighing box.

Question 8. What is least count?

Answer: The minimum measurement which can be performed by using an instrument in measuring a physical quantity, is called least count of this instrument.

Question 9. What is the minimum length that can be measured by a metre scale correctly?

Answer: The minimum length that can be measured by a metre scale is 0.1 cm or 1 mm.

Question 10. What is the maximum length that can be measured by a metre scale accurately?

Answer: 1 m or 100 cm is the maximum length that can be measured by a metre scale accurately.

Question 11. What is the maximum time that can be measured by a wall clock?

Answer: The maximum time that can be measured by a wall clock is 12 hours.

Question 12. What is the maximum mass that can be measured by a common balance using its weight box?

Answer: The maximum mass that can be measured by a common balance by using its weight box is 211.11 g.

Question 13. What is the use of rider of a common balance?

Answer: Rider is used in a common balance To measure a mass of less than 10 mg.

Question 14. What are the minimum and maximum measurement that can be measured by a measuring cylinder of volume 100 mL and 10 mL?

Answer: The minimum and maximum measurement of volume that can be measured by a measuring cylinder of 100 mL and 10 mL are 1 mL and 0.1 mL; 100 mL and 10 mL respectively.

Question 15. For measuring 72.05 g mass of a body what are the different weights in grams and milligrams to be taken from the weight box?

Answer: The weights that can be used are 50g, 20g, 2g and 50 mg.

Question 16. What can be used to measure the length of a curve line?

Answer: The length of a curve line can be measured by using a thread and a meter scale.

Question 17. What can be done to level the base of a common balance?

Answer: levelling screw can be used to balance the base of a common balance.

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Fill In The Blanks

Question 1. ________ cylinder and stopwatch can be used to measure the rate of flow of water from a tap.

Answer: Measuring

Question 2. _______ time is the minimum possible time that can be measured by a wrist watch.

Answer: 1s

Question 3. ________ is the minimum mass that can be measured by a common balance.

Answer: 10 mg

Question 4. Very small time intervals are measured by _______

Answer: Stopwatch

Question 5. Number of hour hand in stop watch is _______

Answer: Zero

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement State Whether True Or False

Question 1. Common balance is used for the measurement of the weight of an object.

Answer: False

Question 2. Determination of area of a regular shaped sheet can not be done by using a graph paper.

Answer: False

Question 3. Digital clock is used for accurate measurement of time.

Answer: True

Question 4. Common balance can work even in the place where there is no gravity.

Answer: True

Question 5. Volume of an irregular shaped body can be measured by a measuring cylinder.

Answer: True

Question 6. Mass of a body can be measured by a spring balance even in a place where there is no gravity.

Answer: False

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Numerical Examples

Percentage of error in the measurment of length by a metre scale is

= \(\frac{\text { value of the smallest division of the scale }}{\text { measured length }}\) x 100%

Then actual mass of the body m = √m1m2.

A common balance have equal lengths of arms but to different masses of pans.

If m1 and m2 be the measured of a body when it is kept on right and left pan respectively

Percentage of error in the measurement of but of different masses of pans. If m1 and m2 be the measured masses of a body when it is kept on right and left pan respectively.

Then actual mass of the body \(m=\frac{m_1+m_2}{2}\)

Vernier constant (c) = length of 1 main scale division-length of 1 vernier scale division measurement of length (l)= main scale reading + vernier scale reading x vernier constant.

Question 1. The two arms of the balance beam of a common balance are unequal but the masses of the two scale pans are equal. When a body is weighed at first in the left pan and then in the right pan, 8 g and 12.5 g are obtained respectively as masses. What is the real mass of the body?

Answer: If the masses of the body are m1 and m2 in the two cases,

m1 = 8g and m2 = 12.5 g

∴ real mass of the body,

\(m =\sqrt{m_1 m_2}=\sqrt{8 \mathrm{~g} \times 12.5 \mathrm{~g}}\)

= \(\sqrt{100 \mathrm{~g}^2}=10 \mathrm{~g}\)

Question 2. 5.00 cm length is measured by a scale whose vernier constant is 0.01 cm. Find percentage of error in this measurement.

Answer: Maximum possible error in the measurement by this scale is = 0.01 cm.

∴ Percentage of error = \(\frac{0.01}{5.00} \times 100 \%=0.20 \%\)

Question 3. In a measuring cylinder 1 ml is divided into 10 equal divisions. Volume of liquid is measured by it and the reading is 25 ml. Find percentage of error in this measurement.

Answer: Here least count of the measuring cylinder is = \(\frac{1}{10}\) mL = 0.1 mL

Measured volume of the liquid = 25 mL.

∴ Percentage of error in measurement of volume \(\frac{0.1}{25}\) = 0.4

Question 4. The two arms of a common balance are equal but masses of the two pans are different. The measured mass of a body when placed in the left pan is 10 g and that of the body when placed in the right pan is 10.2 g. Find exact mass of the body.

Answer: The measured mass of a body in the two cases are m1 = 10 g and m2 = 10.2 g.

∴ Exact mass of the body

\(m=\frac{m_1+m_2}{2}=\frac{10+10.2}{2}=10.1 \mathrm{~g}\)

Chapter 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement

1. Match the physical quantities in column A with their respective units in coloumn B.

WBBSE Solutions For Class 9 Physical Science Ch 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Match The Column 1

Answer: 1. D, 2. A, 3. B, 4. C

2.

WBBSE Solutions For Class 9 Physical Science Ch 1 Topic C Measurement Of Different Physical Quantities And Errors In Measurement Match The Column 2

Answer: 1. C, 2. A, 3. D, 4. B

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