Newton's Laws for System of Particles

Q. A mass of block $8\text{kg}$ is attached by a rope with other block of mass $4\text{kg}$ as shown in the figure. Find the acceleration of COM of the system.
(Neglect friction everywhere and neglect the mass of the rope and pulley)

1. $\frac{g}{9}$
2. $\frac{g}{3}$
3. $\frac{g}{27}$
4. $\frac{g}{5}$

Q.

Internal forces are the forces which bodies exert on each other when the bodies are a part of the system.

1. True
2. False

Q. A pulley-block system as shown in the figure is released from rest. What is the magnitude of acceleration of $\text{COM}$ of pulley-block system? (Take $g=10{\text{m/s}}^2$)

1. $7{\text{m/s}}^2$
2. $5{\text{m/s}}^2$
3. $3.77{\text{m/s}}^2$
4. $10.5{\text{m/s}}^2$

Q. A bomb kept at rest on a smooth horizontal surface, suddenly explodes then identify the correct statement:

1. $\text{COM}$ of bomb will remain at rest.
2. $\text{COM}$ of bomb will move along the surface with a constant velocity after the explosion.
3. After explosion, all the fragments of bomb will fly in vertically upwards direction.
4. Explosion of bomb will cause the centre of mass of bomb to accelerate.

Q. A uniform rod of mass 'm' and length 'L' is tied to a vertical shaft. It rotates in horizontal plane about the vertical axis at angular velocity $\omega$. How much horizontal force does the shaft excert on the rod?

1. $m{w}^{2}L$
2. $\frac{M{w}^{2}L}{2}$
3. $\frac{m{w}^{2}L}{4}$
4. $zero$

Q. An electric dipole of length $2\text{cm}$ is placed with its axis making an angle of ${30}^{\circ }$ to a uniform electric field having intensity ${10}^5\text{N/C}$. If it experiences a torque of $10\sqrt{3}\text{N-m}$, then the potential energy of the dipole is

1. $-20\text{J}$
2. $-10\text{J}$
3. $-30\text{J}$
4. $-40\text{J}$

Q.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_1$ and $m_2$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

1. $\left(\frac{g(m_2+m_1{)}^2}{(m_1-m_2{)}^2}\right)$

2. $(m_1+m_2)g$

3. $\left(\frac{g(m_1+m_2{)}^2}{\left(2m_1{m}_2\right)}\right)$

4. $\left(\frac{(m_2-m_1{)}^{2}g}{(m_1+m_2{)}^2}\right)$

Q.

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

1. Linear momentum of the system does not change in time.

2. Kinetic energy of the system does not change in time.

3. Angular momentum of the system does not change in time.

4. Potential energy of the system does not change in time.

Q. A piece of wood of mass $0.03\text{kg}$ is dropped from the top of a 100 m height building. At the same time, a bullet of mass $0.02\text{kg}$ is fired vertically upward with a velocity $100{\text{ms}}^{-1}$ from the ground. The bullet after collision gets embedded in the wood. Then, the maximum height to which the combined system reaches above the top of the building before falling below is $\text{Take, g}=10m{s}^{-2})$

1. $20\text{m}$
2. $30\text{m}$
3. $10\text{m}$
4. $40\text{m}$

Q. A plank of mass $M$ and length $L$ is at rest on a frictionless floor. The top surface of the plank has friction. At one end of it a man of mass $m$ is standing as shown in Figure. If the man walks towards the other end, find the distance, which the plank moves (a) till the man reaches the centre of the plank, (b) till the man reaches the other end of the plank.

1. $\frac{2mL}{(m+M)}$ and $\frac{mL}{2(m+M)}$
2. $\frac{mL}{2(m+M)}$ and $\frac{2mL}{(m+M)}$
3. $\frac{2mL}{(m+M)}$ and $\frac{mL}{2(m+M)}$
4. $\frac{mL}{2(m+M)}$ and $\frac{mL}{(m+M)}$

Q.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_1$ and $m_2$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

1. $\left(\frac{g(m_2+m_1{)}^2}{(m_1-m_2{)}^2}\right)$

2. $(m_1+m_2)g$

3. $\left(\frac{g(m_1+m_2{)}^2}{\left(2m_1{m}_2\right)}\right)$

4. $\left(\frac{(m_2-m_1{)}^{2}g}{(m_1+m_2{)}^2}\right)$

Q. The velocity of the centre of mass of a system changes from $\overrightarrow{v_1}=4\hat{i}\text{m/s}$ to $\overrightarrow{v_2}=3\hat{j}\text{m/s}$ during time $\Delta t=2\text{s}$. If the mass of the system is $m=10\text{kg}$, the magnitude of constant force acting on the system is

1. $25\text{N}$
2. $20\text{N}$
3. $50\text{N}$
4. $5\text{N}$

Q. Two blocks $A$ and $B$ each of equal mass $m$ are released from the top of a smooth fixed wedge as shown in figure. Find the magnitude of acceleration of $COM$ of the two blocks.

1. $2g$
2. $g$
3. $\frac{2g}{3}$
4. $\frac{g}{2}$

Q.

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the acceleration of the centre of mass of the two blocks.

1. $\frac{g}{4}$

2. $\frac{g}{2}$

3. $\frac{g}{6}$

4. g

Q. Figure below shows two blocks of masses 5 kg and 2 kg placed on a frictionless surface and connected with a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. Deduce (a) velocity gained by the centre of mass and (b) the separate velocities of the two blocks in the centre of mass coordinates just after the kick.

1. 10 m/s, 14 m/s, 10 m/s
2. 10 m/s, 4 m/s, 10 m/s
3. 10 m/s, 4 m/s, -10 m/s
4. 10 m/s, 10 m/s, 10 m/s

Q. Two particles of masses $m$ and $2m$ start moving from origin with same constant speed along $x$ and $y$ axis respectively. The centre of mass of system of particles will move along the line

1. $3y=x$
2. $y=3x$
3. $y=2x$
4. $y=\frac{2x}{5}$