One end of a string of length l is connected to a particle of mass m and the other 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) is:

(i) T, (ii) T - mv² / l, (iii) T + mv² / l, (iv) 0,

T is the tension in the string.

[Choose the correct alternative].

Solution

i) T is the correct answer.
A particle connected to a string is revolving in a circular orbit around the center.
For rotation, the centripetal force is provided by the tension produced in the string.
Therefore, the net force produced on the particle is the tension, T.
That is,
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where,
F is the net force acting on the particle.