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 A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by

Options

A. `2pisqrt(MetaL)`
B. `2pisqrt(M-eta)`
C. `2pi(sqrt(M-L))/(eta)`
D. `2pisqrt((M)/(etaL))`

Answer

D

Explanation

When a force is applied on cubical block A in the horizontal direction, then the lower block B will get distorted as shown by the dotted lines and A will attain a new position (without distortion as A is a rigid body) as shown by the dotted lines.For cubical block B,
`eta=(F//A)/(DeltaL//L)=(F)/(A)xx(L)/(DeltaL)=(F)/(L^(2))xx(L)/(DeltaL)=(F)/(LxxDeltaL)`
implies `F=etaLDeltaL`
eta L ia a constant
implies `FpropDeltaL` and directed towards the mean position
implies oscillation will be simple harmonic in nature . Here, `Momega^(2)=etaL`
implies `omega=sqrt((etaL)/(M))` implies `T=2xxsqrt((M)/(etaL))`