Q. A highly rigid cubical block A of small mass M and side L is fixed rigidly on the cubical block of same dimensions and 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 A small force F is applied perpendicular to one of the side faces of A. after the force is withdrawn, block A executes small oscillations, the time period of which is given by
A) $2\pi\sqrt{ML\eta}$
B) $2\pi\sqrt{M\eta/L}$
C) $2\pi\sqrt{ML/\eta}$
D) $2\pi\sqrt{M/\eta}L$
Explanation
(d) When the force $F$ is applied to one side of block A, let the upper face of $A$ be displaced through distance $\mathrm{\Delta}L$
Then
[image:14_image75.emf]
$\eta = \frac{F/L^{2}\ }{\mathrm{\Delta}L/L}\ \ or\ \ F = \eta L\mathrm{\Delta}L$ …(i)
So, $F \propto \mathrm{\Delta}L$ and this force is restoring one. So, if the force is removed, the block will execute SHM
From Eq. (i) spring factor $= \eta L$
Here, inertia factor$= M$
$\therefore$ Time period, $T = 2\pi\sqrt{\frac{M}{\eta L}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.