Traffic is moving at 60 km/hr along a circular track of radius 0.2 km, the correct angle of banking is

1.  ${\tan }^{-1}\left(\frac{60}{9.8\times 0.2}\right)$

2.  ${\tan }^{-1}\left(\frac{60\times 9.8}{200}\right)$

3.  ${\tan }^{-1}\left(\frac{{\left({\displaystyle \frac{50}{3}}\right)}^2}{200\times 9.8}\right)$

4.  ${\tan }^{-1}\left(\frac{{\displaystyle \frac{50}{3}}}{200\times 9.8}\right)$

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 ${60}^0$ 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 θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\mathrm{\theta }$ for the block to remain stationary on the wedge is:
         

1. $a=\frac{g}{\cos ec\theta }$

2. $a=\frac{g}{\sin \theta }$

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. \(\sqrt{\operatorname{gR}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
2. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)
3. \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\)
4. \(\sqrt{\mathrm{gR}^2\left(\frac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\)

Three blocks A, B, and C of masses 4 kg, 2 kg, and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied to the 4kg block, then the contact force between A and B is: 
       

1. 2 N

2. 6 N

3. 8 N

4. 18 N

A block A of mass ${\mathrm{m}}_1$ 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 B of mass m₂ is suspended. The coefficient of kinetic friction between block A and the table is ${\mathrm{\mu }}_{\mathrm{k}}$. When block A is sliding on the table, the tension in the string is:

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: