Question

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 After the force is withdrawn , block `A` executes faces of `A`. After the force is withdrawn , block `A` exceutes small oscillations , the time period of which is given by
A. `sqrt(eta mL)`
B. `2pisqrt(m(eta)/(L))`
C. `2pisqrt(((mL)/(eta)))`
D. `2pisqrt(((m)/(etaL)))`

Answer 1

Correct Answer - D
Stress `=(F)/(L^(2)),eta=(F)/(L^(2)phi)`
`F=L^(2)eta phi`
`F=L^(2)eta((-x)/(L))" "[because "Strain"=phi=-(x)/(L)]`
`F=(L eta)(-x)`
`rArr" "ma=(Leta)(-x)`
`a=((Leta)/(m))(-x)`
`therefore" "a prop-omega^(2)x`
`(Leta)/(m)(-x)=-omega^(2)x`
or `omega=sqrt(((Leta)/(m)))thereforeT=2pisqrt(((m)/(etaL)))`