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.	\(\dfrac{Mv}{3}\)

Which one of the following statements is incorrect?

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. \(a = g\tan\theta\)

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. \(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)

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 block \(\mathrm{A}\) of mass \(m_1\) rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block \(\mathrm{B}\) of mass \(m_2\) is suspended. The coefficient of kinetic friction between block \(\mathrm{A}\) and the table is \(\mu_k\). When block \(\mathrm{A}\) is sliding on the table, the tension in the string is:
1. \( \dfrac{\left({m}_2+\mu_{{k}}{m}_1\right) {g}}{\left({m}_1+{m}_2\right)}\)

2. \( \dfrac{\left({m}_2-\mu_{{k}} {m}_1\right) {g}}{\left({m}_1+{m}_2\right)}\)

3. \(\dfrac{{m}_1 {~m}_2\left(1-\mu_{{k}}\right) {g}}{\left({m}_1+{m}_2\right)}\)

4. \( \dfrac{{m}_1 {~m}_2\left(1+\mu_{{k}}\right)}{{m}_1+{m}_2} {g}\)

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

Three blocks with masses \(m\), \(2m\), 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 constant speed \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity)

           

1.	\(2~mg\)	2.	\(3~mg\)
3.	\(6~mg\)	4.	zero

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: