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.	\(\frac{Mv}{2}\)	4.	\(\frac{Mv}{3}\)

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:
         

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. \(18~\text{N}\)

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

The force \(\mathrm{F}\) acting on a particle of mass \(\mathrm{m}\) 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:
        

The upper half of an inclined plane of inclination \(\theta\) is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:
1. \(\mu=2/tan \theta\)
2. \(\mu=2tan \theta\)
3. \(\mu=tan \theta\)
4. \(\mu=1/tan \theta\)

A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:

A block of mass \(\mathrm{m}\) is in contact with the cart C as shown in the figure. 
        
The coefficient of static friction between the block and the cart is $\mathrm{\mu }$. The acceleration $\mathrm{\alpha }$ of the cart that will prevent the block from falling satisfies:
1. $\mathrm{\alpha }>\frac{\mathrm{mg}}{\mathrm{\mu }}$

2. $\mathrm{\alpha }>\frac{\mathrm{g}}{\mathrm{\mu m}}$

3. $\mathrm{\alpha }\ge \frac{\mathrm{g}}{\mathrm{\mu }}$

4. $\mathrm{\alpha }<\frac{\mathrm{g}}{\mathrm{\mu }}$

A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)

A tube of length \(\text L\) is filled completely with an incompressible liquid of mass \(\text M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is: