## Statics Multiple Choice Questions And Answers

**Question 1. Two particles, initially at rest, due to their mutual attraction, move towards each other. When their relative velocity becomes v, the velocity of the centre of mass of the system becomes**

- Zero
- v
- 1.5 v
- 3v

**Answer:** 1. Zero

**Question 2. Position vectors of two equal masses with respect to the origin are \(\vec{a}\) and \(\vec{t}\) respectively. The position vector of the centre of mass of these masses is**

- \(\vec{a}+\vec{b}\)
- \(\frac{\vec{a}+\vec{b}}{2}\)
- \(\vec{a} \times \vec{b}\)
- \(\frac{\vec{b}-\vec{a}}{2}\)

**Answer:** 2. \(\frac{\vec{a}+\vec{b}}{2}\)

**Question 3. Position vector of the centre of mass of a system of N particles of total mass M is**

- \(\frac{\sum M \vec{r}_p}{M}\)
- \(\frac{\sum_{p=1}^N \vec{r}_p}{r}\)
- \(\frac{\sum_{p=1}^N m_p \vec{p}_p}{\sum_{p=1}^N m_p}\)
- \(\frac{\sum_{p=1}^N m_p \vec{r}_p}{\sum_{p=1}^N r_p}\)

**Answer:** 3. \(\frac{\sum_{p=1}^N m_p \vec{p}_p}{\sum_{p=1}^N m_p}\)

**Question 4. A stick is thrown in air. It lands a little away from the thrower. The locus of the path of the centre of mass of the stick will be a parabola**

- In all cases
- Only when the stick is uniform
- If the stick had only linear motion and no rotational motion
- If the stick is of such shape that its centre of mass is on the stick itself and not outside

**Answer:** 1. In all cases

**Question 5. A man is hanging from a rope attached to a balloon containing hot air. The system is at rest in the air. If the man climbs up the rope to the balloon, then the centre of mass of the system**

- Remains at rest
- Moves upwards
- Moves downwards
- First moves up and then moves back to the initial position

**Answer:** 1. Remains at rest

**Question 6. Four masses m, m, 2m and 2m are kept at four vertices of a square of side a. The coordinates of the centre of mass of the system are**

- \(\left(\frac{a}{2}, 2 a\right)\)
- \(\left(\frac{a}{2}, a\right)\)
- \(\left(\frac{a}{2}, \frac{2 a}{3}\right)\)
- \(\left(a, \frac{a}{3}\right)\)

**Answer:** 3. \(\left(\frac{a}{2}, \frac{2 a}{3}\right)\)

**Question 7. All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is**

- =R
- ≤R
- >R
- ≥R

**Answer:** 2. ≤R

**Question 8. Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration \(\vec{a}\). The centre of mass has an acceleration**

- Zero
- \(\frac{1}{2} \vec{a}\)
- \(\vec{a}\)
- \(2 \vec{a}\)

**Answer:** 2. \(\frac{1}{2} \vec{a}\)

**Question 9. A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards**

- Heavier piece
- Lighter piece
- Does not shift horizontally
- Depends on the vertical velocity at the time of breaking

**Answer:** 3. Does not shift horizontally

**Question 10. A uniform metal disc of radius R is taken and out of it, a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be**

- \(\frac{R}{4}\) from the centre
- \(\frac{R}{3}\) from the centre
- \(\frac{R}{5}\) from the centre
- \(\frac{R}{6}\) from the centre

**Answer:** 4. \(\frac{R}{6}\) from the centre

**Question 11. The centre of mass of a solid cone along the line from the centre of the base to the vertex is at**

- One-fourth of the height
- One-third of the height
- One-fifth of the height
- None of these

**Answer:** 1. One-fourth of the height

**Question 12. A pulley fixed to the ceiling carries a string with blocks of masses m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of the centre of mass will be**

- Zero
- \(\frac{g}{4}\)
- \(\frac{g}{2}\)
- –\(\frac{g}{2}\)

**Answer:** 3. \(\frac{g}{2}\)

**Question 13. Two particles each of mass 1 g are placed at distances of 1m and 3m respectively from the origin along x -the axis. The centre of mass of the system from the origin is**

- 1 m
- 2 m
- 2.5 m
- 3.5 m

**Answer:** 2. 2 m

**Question 14. A uniform metre scale of mass m is suspended horizontally by two vertical ropes fitted at its two ends. An object of mass 2 m is placed at the 75 cm mark on the scale. The ratio of tension in the two strings is**

- 1:2
- 1:3
- 2:3
- 3:4

**Answer:** 1. 1:2

**Question 15. The height of a solid cone is h and the radius of its circular base is r. The cone has been placed on its base on an inclined plane. The maximum angle of inclination for which the cone will not topple over is**

- \(\cos ^{-1} \frac{2 r}{h}\)
- \(\tan ^{-1} \frac{4 r}{h}\)
- \(\tan ^{-1} \frac{3 r}{h}\)
- \(\sin ^{-1} \frac{4 r}{h}\)

**Answer:** 3. \(\tan ^{-1} \frac{3 r}{h}\)

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

**Question 16. Four forces act on a point object. The object will be in equilibrium, if**

- All of them are in the same plane
- They are opposite to each other in pairs
- The sum of x, y and z components of forces is zero separately
- They form a closed figure of 4 sides when added as per polygon law.

**Answer: **

2. They are opposite to each other in pairs

3. The sum of x, y and z components of forces is zero separately

4. They form a closed figure of 4 sides when added as per polygon law.

**Question 17. The surfaces shown are smooth. The system is released from rest, x-and y-components of acceleration of the centre of mass are**

- \(\left(a_{\mathrm{cm}}\right)_x=\frac{m_1 m_2 g}{m_1+m_2}\)
- \(\left(a_{c m}\right)_x=\frac{m_1 m_2 g}{\left(m_1+m_2\right)^2}\)
- \(\left(a_{\mathrm{cm}}\right)_y=\left(\frac{m_2}{m_1+m_2}\right)^2 g\)
- \(\left(a_{\mathrm{cm}}\right)_y=\left(\frac{m_2}{m_1+m_2}\right) g\)

**Answer:**

2. \(\left(a_{c m}\right)_x=\frac{m_1 m_2 g}{\left(m_1+m_2\right)^2}\)

3. \(\left(a_{\mathrm{cm}}\right)_y=\left(\frac{m_2}{m_1+m_2}\right)^2 g\)

**Question 18. A block of mass m is placed at rest on a smooth wedge of mass M placed at rest on a smooth horizontal surface. As the system is released**

- The centre of mass of the system remains stationary
- The centre of mass of the system has an acceleration g vertically downward
- The momentum of the system is conserved along the horizontal direction
- Acceleration of centre of mass is vertically downward (a < g)

**Answer:**

3. The momentum of the system is conserved along the horizontal direction

4. Acceleration of centre of mass is vertically downward (a < g)