In the shown system, each of the blocks is at rest. The value of \(\theta\) is:
 
1. \(\tan^{- 1} \left(1\right)\)
2. \(\tan^{- 1} \left(\frac{3}{4}\right)\)
3. \(\tan^{- 1} \left(\frac{4}{3}\right)\)
4. \(\tan^{- 1} \left(\frac{3}{5}\right)\)

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 \(g = 10~\text{m/s}^2\), pulleys and strings are ideal and plane is smooth)

 
1. \(\sqrt{\frac{6}{5}}~\text{m/s}\)
2. \(\sqrt{\frac{3}{2}}~\text{m/s}\)
3. \(\sqrt{\frac{5}{6}}~\text{m/s}\)
4. \(\sqrt{\frac{2}{3}}~\text{m/s}\)

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

The pulleys and string shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be:

      

1. 0°
2. 30$°$
3. 45$°$
4. 60$°$

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination $\alpha$ with acceleration $a_0$ is 

1. $\theta ={\tan }^{-1} \alpha$

2. $\theta ={\tan }^{-1} \left(\frac{a_0}{g}\right)$

3. $\theta ={\tan }^{-1} \left(\frac{g}{a_0}\right)$

4. $\theta ={\tan }^{-1} \left(\frac{a_0+g \sin \alpha }{g \cos \alpha }\right)$