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 $\sqrt{7\mathrm{gr}}$ at the lowest point. The tension in the string at the lowest point is:

1. 6mg 

2. 7mg

3. 8mg

4. 1mg 

One end of the string of length ‘l’ is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed 'v', the net force on the particle (directed towards the centre) will be: (T represents the tension in the string)

1. $T+\frac{m{v}^2}{l}$

2. $T-\frac{m{v}^2}{l}$

3. Zero

4. T

A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will
       
1. decrease by a factor of 2
2. remain constant
3. increase by a factor of 2
4. increase by a factor of 4

A mass is performing a vertical circular motion. (see figure) If the average velocity of the particle is increased, then at which point the string will break ?

1. A

2. B

3. C

4. D