As shown in the figure, two masses of 10 kg and 20 kg, respectively are connected by a massless spring. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has an acceleration of 12 m/s² towards the right. The acceleration of 20 kg mass at this instant is:
        
1. 12 m/s² 

2. 4 m/s² 

3. 10 m/s² 

4. Zero

A point mass 'm' is moved in a vertical circle of radius 'r' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point will be:

1. 6 mg

2. 7 mg

3. 8 mg

4. 1 mg

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]

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

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

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.