Question

A block of mass $m$ is suspended by means of an ideal spring of force constant $k$ from ceiling of a car which is moving along a circular path of radius ${}^{\prime }{r}^{\prime }$ with acceleration ${}^{\prime }{a}^{\prime }$. The time period of oscillation of the block when it is displaced along the spring, will be

• A. $2\pi \sqrt{\frac{mg+ma}{k}}$
• B. $2\pi \sqrt{\frac{m}{k\sqrt{g^2+a^2}}}$
• C. $2\pi \sqrt{\frac{m}{k}}$
• D. $2\pi \sqrt{\frac{m}{\sqrt{k^2+g^2+a^2}}}$

Answer 1

Answer: (C)

$2\pi \sqrt{\frac{m}{k}}$

The mass will be acted upon by two acceleration one pseudo acceleration 'a' opposite to the motion of car. It is in a horizontal direction. One in downward direction 'g'.

Resultant of this acceleration

$g^1=\sqrt{g^2+a^2}\left|{}^{\prime }g\perp a^{\prime }\right|But,T=2\pi \sqrt{\frac{m}{k}}$

Hence we have seen that there is no effect of car motion on time period of oscillation of mass attached to string.