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.)

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. \(6~\text{N-s}\)

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 \(m\) is in contact with the cart \((C)\) as shown in the figure. 
                    
The coefficient of static friction between the block and the cart is \(\mu.\) The acceleration \(a\) of the cart that will prevent the block from falling satisfies:
1. \(a > \dfrac{mg}{\mu}\)
2. \(a > \dfrac{g}{\mu m}\)
3. \(a \ge \dfrac{g}{\mu}\)
4. \(a < \dfrac{g}{\mu}\)

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:
         

A body of mass \(5\) kg is suspended by the strings making angles $\mathrm{}$\(60^\circ\) and $\mathrm{}$\(30^\circ\) with the horizontal.

 
Then:

The banking angle for a curved road of radius \(490\) m for a vehicle moving at \(35\) m/s is:
1. ${\tan }^{-1}(0.25)$
2. ${\tan }^{-1}(0.55)$
3. ${\tan }^{-1}(0.45)$
4. ${\tan }^{-1}(0.75)$

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

Two stones of masses \(m\) and \(2m\) are whirled in horizontal circles, the heavier one in a radius \(\frac{r}{2}\) and the lighter one in the radius \(r.\) The tangential speed of lighter stone is \(n\) times that of heavier stone when they experience the same centripetal forces. The value of \(n\) is: