At a given instant, A is moving with velocity of 5 m/s upwards. What is velocity of B at this time?

1. 15 m/s $\downarrow$

2. 15 m/s $\uparrow$

3. 5 m/s $\downarrow$

4. 5 m/s $\uparrow$

The blocks A and B are shown in figure have masses 5 kg and 4 kg respectively. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is (take g = 10 $m/s^2$, pulleys and strings are ideal and plane is smooth)

1. $\sqrt{\frac{6}{5}} m/s$

2.  $\sqrt{\frac{3}{2}} m/s$

3. $\sqrt{\frac{5}{6}} m/s$

4. $\sqrt{\frac{2}{3}} m/s$

In the shown system, each of the block is at rest. The value of $\mathrm{\theta }$ is:
        
1. ${\tan }^{-1}\left(1\right)$

2. ${\tan }^{-1}\left(\frac{3}{4}\right)$

3. ${\tan }^{-1}\left(\frac{4}{3}\right)$

4. ${\tan }^{-1}\left(\frac{3}{5}\right)$

A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of \(a.\) In the frame of the truck, the pendulum will tilt:

A body of mass m is kept on a rough horizontal surface (coefficient of friction = $\mu$). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $\overrightarrow{F}$, where:

1. $\left|\overrightarrow{F}\right|=mg+\mu mg$

2. $\left|\overrightarrow{F}\right|=\mu mg$

3. $\left|\overrightarrow{F}\right|\le mg\sqrt{1+{\mu }^2}$

4. $\left|\overrightarrow{F}\right|=mg$

A block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with retardation a, the acceleration of the block relative to the incline is:

1.  (g + a) sin $\mathrm{\theta }$              
2.  (g – a)
3.  g sin $\mathrm{\theta }$
4.  (g – a) sin $\mathrm{\theta }$

The tension in the spring is

1. Zero

2. 2.5 N

3. 5 N

4. 10 N

Two blocks of 4 kg and 6 kg are attached by springs, they are hanging in vertical position, lower spring breaks due to excessive force. Acceleration of 4 kg block just after breaking

1. 15 $m/s^2$

2. 25 $m/s^2$

3. 10 $m/s^2$

4. Zero

In the system shown $m_1>m_2$. System is held at rest by thread BC. Just after lower thread is Burnt.

1. Acceleration of $m_2$ is upward

2. Magnitude of acceleration of both blocks will be $\left(\frac{m_1-m_2}{m_1+m_2}\right)g$

3. Acceleration of $m_1$ will be non-zero

4. Magnitude of acceleration of two blocks will be non-zero and unequal.

System shown in figure is in equilibrium and at rest. The spring and string are massless, now the stringis cut. The acceleration of mass 2m and m just after string is cut will be

1. g/2 upwards, g downwards

2. g upwards, g/2 downwards

3. g upwards, 2g downwards

4. 2g upwards, g downwards