A highly rigid cubical block `A` of small mass `M` and side `L` is fixed rigidly on the other cubical block of same dimensions and of 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 side faces of `A`. After the force is withdrawn , block `A` executes faces of `A`. After the force is withdrawn , block `A` exceutes small oscillations , the time period of which is given by

Options

A. `2pi sqrt(M eta L)`
B. `2pi sqrt((M)/(eta L))`
C. `2pi sqrt((M L)/(eta))`
D. `sqrt((M)/(eta L))`

Answer

B

Explanation

Stress `= F//A`

shear stra, `= theta = (x)/(L), eta = ("stress")/("strain") = (F//A)/(x//L)`
`rArr F = (eta L^(2))/(L) x rArr a = (-eta L x)/(M) rArr vec(a) prop - vec(x)`
Motion is `S.H.M`
Standard equaction is `a = -omega^(2) x rArr omega^(2) = (eta L)/(M)`
`T = (2pi)/(omega) = 2pi sqrt((M)/(eta L))`