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Question

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 η 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 A small force F is applied perpendicular to one of a sides faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by.

A
2πMηL
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B
2πMη/L
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C
2πML/η
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D
2πM/ηL
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Solution

The correct option is D 2πM/ηL
Modulus of rigidity η=FAθ
Here, A=L2
and θ=xL for small θ
Restoring force =F=ηAθ
or acceleration, a=Fm=ηLMxequation(1)
a(x)
Time period, T=2πxa
T=2πMηL

1078505_1010219_ans_3134798ebf7d41ea9b3dba9807a56b49.png

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