Newton's Laws of Motion

Q. A body of mass $m_1$ collides head on elastically with a stationary body of mass $m_2$. If velocities of $m_1$ before and after the collision are $v$ and $–v/3$ respectively then the value of $m_1/m_2$ is

1. $0.5$
2. $4$
3. $1$
4. $2$

Q. In the figure shown below, $m_A=2\text{kg}$ and $m_B=3\text{kg}$. A force $\text{F}=40\text{N}$ is applied on $2\text{kg}$ block as shown. Find the acceleration of COM of the system. (Neglect friction everywhere and assume the string to be inextensible)

1. $1.2{\text{m/s}}^2$
2. $1{\text{m/s}}^2$
3. $2.4{\text{m/s}}^2$
4. $2{\text{m/s}}^2$

Q. Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are placed at rest on a frictionless surface and connected by a spring. An external hit gives a velocity of $21\text{m/s}$ to the heavier block towards the lighter one. Velocities of both blocks (heavier and lighter one) in the centre of mass frame, just after the kick will be respectively:
(Consider direction of motion of heavier block as $+ve$ direction)

1. $6\text{m/s},10\text{m/s}$
2. $6\text{m/s},-15\text{m/s}$
3. $15\text{m/s},15\text{m/s}$
4. $3\text{m/s},5\text{m/s}$

Q. For the arrangement shown in the figure, $m_1=6\text{kg}$ and $m_2=4\text{kg}$. If the string is light and inextensible and the pulley and surfaces are frictionless, find the magnitude of the acceleration of the center of mass.
(Take $g=10m/s^2$)

1. $4{\text{m/s}}^2$
2. $10{\text{m/s}}^2$
3. $6{\text{m/s}}^2$
4. $2.88{\text{m/s}}^2$

Q. For a spring block system as shown in figure, a time varying force $F=5t\text{N}$ is applied on mass $2\text{kg}$. After $10\text{seconds}$, velocity of $3\text{kg}$ mass is $30\text{m/s}$. Find the velocity of $2\text{kg}$ mass at this instant.

1. $40\text{m/s}$
2. $80\text{m/s}$
3. $\frac{80}{3}\text{m/s}$
4. $20\text{m/s}$

Q. A body of mass $10\text{kg}$ moving with velocity of $10\text{m/s}$ hits another body of mass $30\text{kg}$ moving with velocity $3\text{m/s}$ in same direction. The co-efficient of restitution is $\frac{1}{4}$. The velocity of centre of mass after collision will be

1. $20\text{m/s}$
2. $40\text{m/s}$
3. $\frac{19}{4}\text{m/s}$
4. $\frac{23}{4}\text{m/s}$

Q. For a spring block system as shown in figure, a time varying force $F=5t\text{N}$ is applied on mass $2\text{kg}$. After $10\text{seconds}$, velocity of $3\text{kg}$ mass is $30\text{m/s}$. Find the velocity of $2\text{kg}$ mass at this instant.

1. $40\text{m/s}$
2. $80\text{m/s}$
3. $\frac{80}{3}\text{m/s}$
4. $20\text{m/s}$

Q. A man of mass $75\text{kg}$ is standing on a platform of mass $15\text{kg}$ kept on a smooth horizontal surface. The man starts moving on the platform with a velocity of $20\text{m/s}$ relative to the platform. Then, magnitude of the recoil velocity of the platform is

1. $12.33\text{m/s}$
2. $20\text{m/s}$
3. $25\text{m/s}$
4. $16.66\text{m/s}$

Q. Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are placed at rest on a frictionless surface and connected by a spring. An external hit gives a velocity of $21\text{m/s}$ to the heavier block towards the lighter one. Velocities of both blocks (heavier and lighter one) in the centre of mass frame, just after the kick will be respectively:
(Consider direction of motion of heavier block as $+ve$ direction)

1. $6\text{m/s},10\text{m/s}$
2. $6\text{m/s},-15\text{m/s}$
3. $15\text{m/s},15\text{m/s}$
4. $3\text{m/s},5\text{m/s}$

Q. In the figure shown below, $m_A=2\text{kg}$ and $m_B=3\text{kg}$. A force $\text{F}=40\text{N}$ is applied on $2\text{kg}$ block as shown. Find the acceleration of COM of the system. (Neglect friction everywhere and assume the string to be inextensible)

1. $1.2{\text{m/s}}^2$
2. $1{\text{m/s}}^2$
3. $2.4{\text{m/s}}^2$
4. $2{\text{m/s}}^2$

Q. Two blocks are attached to the pulley as shown in the arrangement.

If the string is inextensible and all surfaces are frictionless, find out the magnitude acceleration of COM of the system. (Take $g=10m/s^2$)

1. $1.6{\text{m/s}}^2$
2. $0.4{\text{m/s}}^2$
3. $0.16{\text{m/s}}^2$
4. $4{\text{m/s}}^2$

Q. A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v\left(x\right)=$ $b{x}^{-2n}$, where $b$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

Q. A particle of mass $m$ is moving with a constant acceleration $2a$ towards another particle of mass $4m$ as shown in figure. Mass $4m$ is also moving with acceleration $a$ towards the particle of mass $m$. Find the acceleration of $COM$ of the system.

1. $a/5$ (towards left)
2. $2a/5$ (towards left)
3. $a/5$ (towards right)
4. $2a/5$ (towards right)

Q. A man wearing a bullet-proof vest stands still on roller skates. The total mass is $80\text{kg}$. A bullet of mass $20$ grams is fired at $400\text{m/s}$. It is stopped by the vest and man falls to the ground. What is then, the velocity of man ?

1. $1\text{m/s}$
2. $0.1\text{m/s}$
3. $2\text{m/s}$
4. $2.5\text{m/s}$

Q. A pulley mass arrangement is shown is the figure. A force of $50\text{N}$ is applied on the $2\text{kg}$ block. Find the acceleration of COM of the system.

1. $1.6{\text{m/s}}^2$
2. $2{\text{m/s}}^2$
3. $10{\text{m/s}}^2$
4. $0{\text{m/s}}^2$

Q. A man wearing a bullet-proof vest stands still on roller skates. The total mass is $80\text{kg}$. A bullet of mass $20$ grams is fired at $400\text{m/s}$. It is stopped by the vest and man falls to the ground. What is then, the velocity of man ?

1. $1\text{m/s}$
2. $2\text{m/s}$
3. $2.5\text{m/s}$
4. $0.1\text{m/s}$