Please be patient as the PDF generation may take up to a minute.

1.

A block of mass \(m\) is placed on a smooth inclined wedge \(ABC\) of inclination \(\theta\) as shown in the figure. The wedge is given an acceleration '\(a\)' towards the right. The relation between \(a\) and \(\theta\) for the block to remain stationary on the wedge is:

1.	\(a = \dfrac{g}{\mathrm{cosec }~ \theta}\)	2.	\(a = \dfrac{g}{\sin\theta}\)
3.	\(a = g\cos\theta\)	4.	\(a = g\tan\theta\)

2. A box of mass \(5 ~\text{kg}\) is pulled by a cord, up along a frictionless plane inclined at \(30^\circ\) with the horizontal. The tension in the cord is \(30~\text N.\) The acceleration of the box is: (take \(g=10~\text{ms}^{-2}\))

1.	\(2~\text{ms}^{-2}\)	2.	zero
3.	\(0.1~\text{ms}^{-2}\)	4.	\(1~\text{ms}^{-2}\)

3.

A particle moving with velocity \(\vec{v}\) is acted by three forces shown by the vector triangle \({PQR}.\) The velocity of the particle will:
     

1.	change according to the smallest force \({\overrightarrow{Q R}}\)
2.	increase
3.	decrease
4.	remain constant

4.

Three blocks \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{C}\) of masses \(4~\text{kg}\), \(2~\text{kg}\), and \(1~\text{kg}\) respectively, are in contact on a frictionless surface, as shown. If a force of \(14~\text{N}\) is applied to the \(4~\text{kg}\) block, then the contact force between \(\mathrm{A}\) and \(\mathrm{B}\) is: 
       
1. \(2~\text{N}\)
2. \(6~\text{N}\)
3. \(8~\text{N}\)
4. \(18~\text{N}\)

5.

If the block is being pulled by the rope moving at speed \(v\) as shown, then the horizontal velocity of the block is:
 
1. \(v\)
2. \(v\cos\theta\)
3. \(\frac{v}{\cos\theta}\)
4. \(\frac{v}{\sin\theta}\)

6.

A system consists of three masses \(m_1,\) \(m_2,\) and \(m_3\) connected by a string passing over a pulley \(\mathrm{P}.\) The mass \(m_1\) hangs freely, and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction \(=\mu.\)) The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is:
(Assume \(m_1=m_2=m_3=m\) and \(g\) is the acceleration due to gravity.)

1.	\(\dfrac{g(1-g \mu)}{9}\)	2.	\(\dfrac{2 g \mu}{3}\)
3.	\( \dfrac{g(1-2 \mu)}{3}\)	4.	\(\dfrac{g(1-2 \mu)}{2}\)

7.

As shown in the figure, two masses of \(10~\text{kg}\) and \(20~\text{kg}\), respectively are connected by a massless spring. A force of \(200~\text{N}\) acts on the \(20~\text{kg}\) mass. At the instant shown, the \(10~\text{kg}\) mass has an acceleration of \(12~\text{m/s}^2\) towards the right. The acceleration of \(20~\text{kg}\) mass at this instant is:
          
1. \(12~\text{m/s}^2\)
2. \(4~\text{m/s}^2\)
3. \(10~\text{m/s}^2\)
4. zero

8. A car is moving in a circular horizontal track of radius \(10~\text m\) with a constant speed of \(10~\text{m/s}.\) A bob is suspended from the roof of the car by a light wire of length \(1.0~\text m.\) The angle made by the wire with the vertical is: 

1.	\(\dfrac{\pi}{3} \)	2.	\(\dfrac{\pi}{6}\)
3.	\(\dfrac{\pi}{4}\)	4.	\(0^\circ\)

9.

A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:

1.	\(\sqrt{\operatorname{gR}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)	2.	\(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
3.	\(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\)	4.	\(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)

10.

Three blocks with masses of \(m\), \(2m\), and \(3m\) are connected by strings as shown in the figure. After an upward force \(F\) is applied on block \(m\), the masses move upward at a constant speed, \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity).