A uniform pole of length $2 L$ is laid on a smooth horizontal table as shown in figure. The mass of pole is $M$ and it is connected to a frictionless axis at $O$ . A spring with force constant $k$ is connected to the other end. The pole is displaced by a small angle $θ$ from equilibrium position and released such that it performs small oscillations. Its frequency of oscillations

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$ω = \sqrt{\frac{k}{2 M}}$

$ω = \sqrt{\frac{M}{3 k}}$

$ω = \sqrt{\frac{k}{3 M}}$

$ω = \sqrt{\frac{3 k}{M}}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The restoring torque for small $θ$

$τ_{r e s t} = - [k (2 L θ) \times 2 L]$

and $α = \frac{τ_{r e s t}}{I}$

$= \frac{4 k L^{2}}{\frac{M {(2 L)}^{2}}{3}} (- θ) = \frac{3 k}{M} (- θ)$

On comparing with $α = - ω^{2} θ$ , we get

$ω = \sqrt{\frac{3 k}{M}}$

Watch 3-min video & get full concept clarity