Question

A highly rigid cubical block A of small mass M and side L is fixed rigidly on the another cubical block of same dimensions and of low modulus of rigidity h such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on the horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A excutes small oscillations, the time period of which is given by –

• A. $2\pi\sqrt{(M\eta L)}$
• B. $2\pi\sqrt{(M\eta/L)}$
• C. $2\pi\sqrt{(ML/\eta)}$
• D. $2\pi\sqrt{(M/L\eta)}$

Answer 1

Answer: (D)

$2\pi\sqrt{(M/L\eta)}$

Answer 2

$\mathrm { t } \propto [ \mathrm { M } ] ^ { \mathrm { a } } [ \eta ] ^ { \mathrm { b } } [ \mathrm { L } ] ^ { \mathrm { c } }$ $M^{0}L^{0}T^{1} \propto$$M^{0}L^{0}T \propto M^{a + b}L^{- b + c}T^{- 2b}$

Equating dimensions of both sides.

a + b = 0 ̃ a = –b

–b + c = 0 ̃ b = c

–2b = 1 ̃ b = –1/2

\ a = 1/2, c = –1/2

Therefore t µ M^1/2[h]^–1/2[L]^–1/2

T µ $\sqrt{\frac{M}{\eta L}}$.