Question

A string of length $\ell$ has one end fixed and a particle of mass m is attached to the other end. If the particle describe a horizontal circle at an angular speed $\omega$, in gravity free space.

• A. The tension in the string = $m{\omega }^2\ell$
• B. The speed of the particle is $\ell \omega$
• C. The resultant force acting on the particle has no vertical component
• D. None of these

Answer 1

Answer: (A), (B), (C)

The resultant force acting on the particle has no vertical component
The speed of the particle is $\ell \omega$
The tension in the string = $m{\omega }^2\ell$

When a move in circular motion, centripetal force will act on the body toward center.

When body moves with uniform angular velocity in circular path.

Then,

(i) Centripetal force, $F_c=m\omega l^2$

(ii) Speed of the particle, $v=\omega l$

(iii) Because it is horizontal circle and there is no gravity. Therefore there is no force in vertical direction.