Question

A uniform rod can rotate freely about one end. Rod is in equilibrium with the
help of massless spring in horizontal position. Then
(mass of rod=m; length of rod =/; spring constant=k).
31​

Answer 1

Explanation:

If the rod is rotated through an angle θ, extension in one spring = compression in the other spring,

i.e.,x=lθ/2

Therefore, force acting on each of the ends of the rod,

F=kx=k(lθ/2)

Restoring torque on the rod,

T=−Fl=−k( θ/2)l=−kl

2

(θ/2)

As T=Iα=(Ml

2

/12)α

or α=−

M

6k

θ,α∝theta.

Thus, the motion of the rod is simple harmonic with

ω

2

=

M

6k

orω=

M

6k

orv=

2π

1

M

6k