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 the side faces of A . After the force is withdrawn, block A executes small oscillations, the time period of which is given by

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 the side faces of A . After the force is withdrawn, block A executes small oscillations, the time period of which is given by, 2 π M η L, 2 π M η L, 2 π M L η, 2 π M η L

MARKS App · Accepted Answer

Modulus of rigidity, η = F A . θ Here, A = L 2 And θ = x L Therefore, restoring force is F = − η A θ = − η L x Or acceleration, a = F M = − η L M x Since, a ∝ x , oscillations are simaple harmonic in nature, time period of which is given by T = 2 π | d i s p l a c e m e n t a c c e l e r a t i o n | = 2 π | x a | = 2 π M η L

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