## Circular Motion Multiple Choice Questions And Answers

**Question 1. A wheel is rotating 300 times per minute. The angular velocity of the wheel in rad • s ^{-1} unit is**

- 10π
- 20π
- 30π
- 5π

**Answer:** 1.10π

**Question 2. Two bodies of masses m _{1 }and m_{2} are moving at uniform speed along circular paths of radii r_{1} and r_{2} respectively. If they take equal time to describe the circles completely, the ratio of their angular velocities will be**

- \(\frac{r_1}{r_2}\)
- \(\frac{m_1}{m_2}\)
- \(\frac{m_1 r_1}{m_2 r_2}\)
- 1

**Answer:** 4. 1

**Question 3. If a body travels along a circular path with uniform speed then its acceleration**

- Acts along its circumference
- Acts along its tangent
- Acts along its radius
- Is zero

**Answer:** 3. Acts along its radius

**Question 4. After switching on a ceiling fan it completes 10 resolutions in 3 s. The number of complete resolutions it will perform in the next 3 s (assuming uniform angular acceleration) is**

- 10
- 20
- 30
- 40

**Answer:** 3. 30

**Question 5. If a wheel revolves 120 times per minute then its angular velocity in rad · s ^{-1} unit is**

- π²
- 2π²
- 4π²
- 8π²

**Answer:** 2. 2π²

**Question 6. The angular velocity of the hour hand of a clock is**

- \(\frac{\pi}{30} \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(2 \pi \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(\frac{\pi}{1800} \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(\frac{\pi}{21600} \mathrm{rad} \cdot \mathrm{s}^{-1}\)

**Answer:** 4. \(\frac{\pi}{21600} \mathrm{rad} \cdot \mathrm{s}^{-1}\)

**Question 7. If a particle rotates along a circular path of radius 25 cm with a frequency of 2 rps, its linear acceleration in m · s ^{-2} unit is**

- π²
- 2π²
- 4π²
- 8π²

**Answer:** 3.

**Question 8. An artificial satellite takes 90 minutes to complete its revolution around the Earth. The angular speed of the satellite is**

- \(\frac{\pi}{1800} \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(\frac{\pi}{2700} \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(\frac{2 \pi}{2700} \mathrm{rad} \cdot \mathrm{s}^{-1}\)
- \(\frac{\pi}{45} \mathrm{rad} \cdot \mathrm{s}^{-1}\)

**Answer:** 2. \(\frac{\pi}{2700} \mathrm{rad} \cdot \mathrm{s}^{-1}\)

**Question 9. The driver of a truck suddenly finds a wall in front of him. To avoid collision with the wall he should**

- Apply brake at once
- Turn speedily in a circular path
- Follow both the processes 1 and 2
- Do none of the above processes

**Answer:** 1. Apply brake at once

**Question 10. Which of the following quantities does not remain constant in a uniform circular motion?**

- Speed
- Momentum
- Kinetic energy
- Mass

**Answer:** 2. Momentum

**Question 11. The angular velocity of a particle, \(\vec{w}=3 \hat{i}-4 \hat{j}+\hat{k}\) and its position vector, \(\vec{r}=5 \hat{i}-6 \hat{j}+6\hat{k}\). What is the linear velocity of the particle?**

- \(-18 \hat{i}+13 \hat{j}+2 \hat{k}\)
- \(18 \hat{i}-13 \hat{j}-2 \hat{k}\)
- \(-18 \hat{i}-13 \hat{j}+2 \hat{k}\)
- \(18 \hat{i}+13 \hat{j}-2 \hat{k}\)

**Answer: **3. \(-18 \hat{i}-13 \hat{j}+2 \hat{k}\)

**Question 12. The ratio of angular speeds of the minute hand and hour hand of a watch is**

- 1:12
- 6:1
- 12:1
- 1:6

**Answer:** 3. 12:1

**Question 13. A panicle moves with constant angular velocity in a circle. During the motion its**

- Energy is conserved
- Momentum is conserved
- Energy and momentum both are conserved
- None of the above

**Answer:** 1. Energy is conserved

**Question 14. The angular speed of a flywheel making 360 revolutions per minute is**

- 12 π rad · s
^{-1} - 6 π rad · s
^{-1} - 3 π rad · s
^{-1} - 2 π rad · s
^{-1}

**Answer:** 1. 12π rad · s^{-1}

**Question 15. A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statements about the velocity of the car is true?**

- The magnitude of velocity is not constant
- Both magnitude and direction of velocity change
- Velocity is directed towards the centre of the circle
- The magnitude of velocity is constant but the direction changes

**Answer:** 4. Magnitude of velocity is constant but the direction changes

**Question 16. A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of the topmost point relative to the bottommost point is**

- v
- 2v
- \(\frac{v}{2}\)
- Zero

**Answer:** 2. 2v

**Question 17. The angle with which a cyclist leans with the horizontally while turning a curved path of radius r with speed v is**

- \(\theta=\tan ^{-1} \frac{v^2}{r g}\)
- \(\theta=\tan ^{-1} v^2 r g\)
- \(\theta=\tan ^{-1} \frac{r g}{v^2}\)
- \(\theta=\tan ^{-1} \frac{r}{v g}\)

**Answer:** 2. \(\theta=\tan ^{-1} v^2 r g\)

**Question 18. While taking a turn on a plane horizontal road, a car can skid due to**

- Gravitational force
- Absence of necessary centripetal force
- Rolling friction between the tyre of the car and the road
- Reaction force of the road

**Answer:** 2. Absence of necessary centripetal force

**Question 19. A car is moving along a horizontal circular path of radius 10 m at a uniform speed of 10 m · s ^{-1}. A pendulum bob is suspended by means of a light rod from the ceiling of the car. The angle made by the rod with the horizontal path will be (g = 10 m s^{-2})**

- Zero
- 30°
- 45°
- 60°

**Answer:** 3. 45°

**Question 20. If maximum and minimum tension in the string whirling in a circle of radius 2.5 m are in the ratio 5 : 3 then its velocity is**

- \(\sqrt{98} \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(7 \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(\sqrt{490} \mathrm{~m} \cdot \mathrm{s}^{-1}\)
- \(\sqrt{4.9} \mathrm{~m} \cdot \mathrm{s}^{-1}\)

Answer: 1. \(\sqrt{98} \mathrm{~m} \cdot \mathrm{s}^{-1}\)

**Question 21. The coefficient of friction between the road and the tyre of a car is 0.6. What is the maximum safe limiting speed with which the car can overcome a bend of radius 150 m?**

- 60m · s
^{-1} - 15m · s
^{-1} - 30 m · s
^{-1} - 25 m · s
^{-1}

**Answer:** 3. 30 m · s^{-1}

**Question 22. A body is moving in a circular path with centripetal acceleration a. If its speed gets doubled, find the ratio of the centripetal acceleration after and before the speed in changed.**

- 1:4
- 1:2
- 2:1
- 4:1

**Answer:** 4. 4:1

**Question 23. A ball of mass 0.12 kg is being whirled in a horizontal circle at the end of a string 0.5 m long. It is capable of making 231 revolutions in one minute. The breaking tension of the string is**

- 3N
- 15.1 N
- 31.5 N
- 35.1 N

**Answer:** 4. 35.1 N

**Question 24. A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m · s ^{-1}. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.0 m. The angle made by the rod with the track is (g = 10 m · s^{-2})**

- Zero
- 30°
- 45°
- 60°

**Answer:** 3. 45°

**Question 25. The motor of an engine is rotating about its axis with an angular velocity of 100 rpm. It comes to rest in 15 s, after being switched off. Assuming constant angular deceleration, what are the numbers of revolutions made by it before coming to rest?**

- 12.5
- 40
- 32.5
- 15.6

**Answer:** 1. 12.5

**In this type of question, more than one option are correct.**

**Question 26. In uniform circular motion of a particle**

- Particles cannot have uniform velocity
- Particles cannot have uniformly accelerated motion
- The particle cannot have net force equal to zero
- Particles cannot have any force in the tangential direction

**Answer:** All options are correct

**Question 27. A particle is moving in a circular path with decreasing speed. For this situation, mark out the correct statements.**

- The radial component of its acceleration is decreasing in magnitude
- The angular speed of the particle is decreasing
- The tangential components of its acceleration and velocity are in opposite directions
- The article is performing a ron-uniform circular motion

**Answer:** All options are correct