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1.

Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:
            

1.	\(\dfrac{g}{2}\)	2.	\(\dfrac{g}{5}\)
3.	\(\dfrac{g}{10}\)	4.	\(g\)

2.

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be: 
 
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

3.

The force \(F\) acting on a particle of mass \(m\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(0\) to \(8\) s is:

1. \(24~\text{N-s}\)
2. \(20~\text{N-s}\)
3. \(12~\text{N-s}\)
4. \(6~\text{N-s}\)

4.

When a body of mass \(m\) just begins to slide as shown, match List-I with List-II:

	List-I		List-II
(a)	Normal reaction	(i)	\(P\)
(b)	Frictional force \((f_s)\)	(ii)	\(Q\)
(c)	Weight \((mg)\)	(iii)	\(R\)
(d)	\(mg \mathrm{sin}\theta ~\)	(iv)	\(S\)

Choose the correct answer from the options given below:

	(a)	(b)	(c)	(d)
1.	(ii)	(i)	(iii)	(iv)
2.	(iv)	(ii)	(iii)	(i)
3.	(iv)	(iii)	(ii)	(i)
4.	(ii)	(iii)	(iv)	(i)

5.

What is the velocity of the block when the angle between the string and the horizontal is \(30^\circ\) as shown in the diagram?

1. \(v_B=v_P\)
2. \(v_B=\frac{v_P}{\sqrt{3}}\)
3. \(v_B=2v_P\)
4. \(v_B=\frac{2v_P}{\sqrt{3}}\)

6.

A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:

1.	\(\sqrt{\dfrac{Rg}{\mu_s} }\)	2.	\(\sqrt{\dfrac{mRg}{\mu_s}}\)
3.	\(\sqrt{\mu_s Rg}\)	4.	\(\sqrt{\mu_s m Rg}\)

7.

A massless and inextensible string connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) of masses \(3m\) and \(m,\) respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of \(\mathrm{A}\) and \(\mathrm{B}\) immediately after the string is cut, are respectively:
      

1.	\(\dfrac{g}{3},g\)	2.	\(g,g\)
3.	\(\dfrac{g}{3},\dfrac{g}{3}\)	4.	\(g,\dfrac{g}{3}\)

8. A bob is whirled in a horizontal plane by means of a string with an initial speed of \(\omega\) rpm. The tension in the string is \(T\). If speed becomes \(2\omega\) while keeping the same radius, the tension in the string becomes:

1.	\(4 T\)	2.	\(\dfrac{T}{4}\)
3.	\(\sqrt{2} T\)	4.	\(T\)

9.

A rigid ball of mass \(M\) strikes a rigid wall at \(60^{\circ}\) and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be:
     

1.	\(Mv\)	2.	\(2Mv\)
3.	\(\dfrac{Mv}{2}\)	4.	\(\dfrac{Mv}{3}\)

10.

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:

1.	to the left and the angle of inclination of the pendulum with the vertical is \(\text{sin}^{-1} \left( \dfrac{a}{g} \right )\)
2.	to the left and the angle of inclination of the pendulum with the vertical is \(\text{cos}^{-1} \left ( \dfrac{a}{g} \right )\)
3.	to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{a}{g} \right )\)
4.	to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \dfrac{g}{a} \right )\)