A highly rigid cubical block (A) of small mass (M) and slide (L) is fixed rigidly on to another cubical block (B) of the same dimesions and of low modulus of rigidity (eta) 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 sides 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 After the force is withdrawn, block (A) executes small oscillations the time period of which is given by.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))`