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. \(mg\)

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 center) 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