Question

# A rigid cubical block A of mass M and side L is fixed rigidly on to another cubical block of the same dimensions and of modulus of rigidity n 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 A small F is applied perpendicular to one of the side faces of A.After the force is withdrawn, block A executes small oscillations, the time period of which is

A
2πMnl
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B
2πMnL
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C
2πMLn
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D
2πMnL
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Solution

## The correct option is D 2π√MnLLet the force F produce a deformation x. When this force is whithdrawn, the force that tries to restore block A to its equilibrium position is proportional to x and is given by f=−ηLx ∴ Acceleration d2xdt2=fM=−ηLMX=−ω2X where ω=√ηLM The angular frequency of this simple harmonic frequency is ω. Now T=2Tω Therefore T=2π√MηL

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