Newton's Laws of Motion

Q.

A mon of mass m moves on a plank of mass M with a constant velocity u eith respect to the plank , as shown in figure.
If the plank rests on a smooth horizontal surface, then determine the velocity of the plank.

1. 

2. 

3. 

4. u

Q. The velocity of point of contact $R$, of the rod just before impact with the bumper is (in m/s):

1. $1.2$
2. $1.2$$\sqrt{5}$
3. $\sqrt{5}$
4. $2.4$

Q. An unbanked curve has a radius of $60m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$, is:

1. $2.1m/s$
2. $145m/s$
3. $21m/s$
4. $7m/s$

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

Q. A force $F$ is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of cart at $t=5\text{sec}$ is -

1. $10\text{m/s}$
2. $\text{Zero}$
3. $2\text{m/s}$
4. $8.33\text{m/s}$

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. $0{\text{m/s}}^2$