In the figure pulley ${\mathrm{P}}_1$ is fixed and the pulley ${\mathrm{P}}_2$ is movable. If ${\mathrm{w}}_1={\mathrm{w}}_2$, what is the angle between ${\mathrm{AP}}_2{\mathrm{P}}_1$? (pulleys are frictionless)

         
1. 30°

2. 60°

3. 150°

4. 120°

A light spring is compressed and placed horizontally between a vertical fixed wall and a toy car which is free to slide over a smooth horizontal table. If the system is released from rest, which graph best represents acceleration $a$ and distance $x$ covered by the car?

1.		2.
3.		4.

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:
         

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 $F$ 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. $6~\text{N-s}$

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