Question

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)

• A. \( T \)
• B. \( T + \frac{m v^2}{l} \)
• C. \( T - \frac{m v^2}{l} \)
• D. zero

Hint:

In circular motion, the net force acting on the particle is the centripetal force, which is provided by the tension in the string. For an object of mass \( m \) moving with speed \( v \) in a circle of radius \( l \), the centripetal force is \( \frac{m v^2}{l} \).

Answer 1

The Correct Option is A

In this problem, the particle is moving in a circular path with radius \( l \) and speed \( v \). The net force acting on the particle is the centripetal force, which is required to keep the particle in circular motion. This force is provided by the tension \( T \) in the string. The centripetal force \( F_c \) is given by: \[ F_c = \frac{m v^2}{l} \] Since the particle is moving in a circle, the tension \( T \) in the string exactly balances this centripetal force, and the net force on the particle is simply \( T \), directed towards the center of the circle. Therefore, the net force on the particle is \( T \).