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 A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by :



Solution

The correct option is D


Modules of rigidity, =FAθ

Here, A=L2 and

θ=xL

Therefore, force, F = -ηAθ=ηLx

Or acceleration, a = FM=ηLM×x

Since, a μx, oscillations are simple harmonic in nature, time period of which is given by

T=2πdisplacmentacceleration=2πxa=2πMηL

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