Three blocks A, B and C of mass 3M, 2M and M respectively are suspended vertically with the help of springs PQ and TU and a string RS as shown in fig. The acceleration of blocks A, B and C are $a_1,a_2 and a_3$ respectively.
     

The value of acceleration \(a_{1}\) at the moment string RS is cut will be: 

1. g downward

2. g upward

3. more than g downward

4. zero

If $\mathrm{\mu }$ between block A and inclined plane is 0.5 and that between block B and the inclined plane is 0.8, then the normal reaction between blocks A and B will be:
                     
1. 180 N

2. 216 N

3. 0

4. None of these

A particle of mass ‘m’ having speed v goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative y-axis is $\theta$ then the tension in the string is:
[Take radius = R]

$1.$ $mg\sin \theta +\frac{m{v}^2}{R}$
$2.\hspace{0.17em}mg\cos \theta -\frac{m{v}^2}{R}$
$3.\hspace{0.17em}\hspace{0.17em}mg\cos \theta +\frac{m{v}^2}{R}$
$4.\hspace{0.17em}\hspace{0.17em}mg\sin \theta -\frac{m{v}^2}{R}$

Calculate the reading of the spring balance shown in the figure: (take \(g=10\) m/s²)
                

1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N

A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
   $\mathrm{}$

The angle of banking for a cyclist taking a turn at a curve is given by tan$\mathrm{\theta } = \frac{{\mathrm{v}}^{\mathrm{n}}}{\mathrm{rg}}$ where symbols have their usual meaning. The value of n is:

A body of mass m is moving on a concave bridge ABC of the radius of curvature R at a speed v. The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1.  $\mathrm{mg}$ $-$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

2.  $\mathrm{mg}$ $+$ $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

3.  mg

4.  $\frac{{\mathrm{mv}}^2}{\mathrm{R}}$

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:

1. moving with constant velocity.

2. in accelerated motion.

3. in retarded motion.

4. at rest.

The kinetic energy 'K' of a particle moving in a circular path varies with the distance covered S as K = a${\mathrm{S}}^2$, where a is constant. The angle between the tangential force and the net force acting on the particle is: (R is the radius of the circular path)

1.  ${\tan }^{-1}\left(\frac{\mathrm{S}}{\mathrm{R}}\right)$

2.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{S}}\right)$

3.  ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{R}}\right)$

4.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{a}}\right)$

Choose the incorrect alternative: