Q. 43.9( 48 Votes )

# 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:

T is the tension in the string. [Choose the correct alternative].

A . T,

B.

C.

D. 0

Answer :

The centripetal force experienced by a particle connected to a string revolving in a circular path around a centre is given by,

Where,

F is the centripetal force acting on the particle

m is the mass of the particle.

v is the speed of the particle and

l is the length of the string.

Here, the tension produces in the spring provides the centripetal force required by the body to stay in a circular motion.

Thus, the net force on the particle is given as,

Where,

T is the tension in the string.

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The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.

(b) Show that F = −mω^{2}r

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