Question

A highly rigid cubical block A of small mass M and side L is fixed rigidly to another cubical block B of the same dimensions and modulus of rigidity η Such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on horizontal surface. A small force is applied perpendicular to one of the side face of A. After the force is withdrawn block A executes small oscillations the time period of which is given by

Answer 1

Answer:

Explanation:

Modulus of rigidity η=FAθ

Here A=L2

and θ=xL for small 'θ'

∴ restoring force =F=−ηAθ

=−ηLx

or acceleration a=Fm

=−ηLMx -------(1)

Since aα−x

Since the acceleration is dependent on the displacement linearly we have simple harmonic motion. and hence the

time period is given by

T=2π∣∣xa∣∣−−−√

=2πMηL−−−√