Question

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is ______.

विकल्प

• `(mlomega^2)/(k - omegam)`

• `(mlomega^2)/(k - momega^2)`

• `(mlomega^2)/(k + momega^2)`

• `(mlomega^2)/(k + momega)`

Answer 1

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is `underlinebb((mlomega^2)/(k - momega^2)).`

Explanation:

At elongated position (x),

 

`F_{radial} = (mv^2)/r = mromega^2`

∴ kx = m(l + x)ω² (∵ r = l + x here)

kx = mlω² + mxω² 

∴ x = `(mlomega^2)/(k - momega^2)`