Question

Two blocks of masses m and M, \((M>M)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then

(\(\mu = \) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)

(B) The acceleration of the blocks is a \(=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\)

(\(x = \) displacement of the blocks from the mean position)

(C) The magnitude of the frictional force on the upper block is \(\frac{\mathrm{m} \mu|\mathrm{x}|}{\mathrm{M}+\mathrm{m}}\)

(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)

(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\)

Choose the correct answer from the options given below :

(1) A, B, D Only

(2) B, C, D Only

(3) C, D, E Only

(4) A, B, C Only

Answer 1

Correct option is : (1) A, B, D Only

Time period \(= 2 \pi \sqrt{\frac{M+m}{K}}\)

\(a = \frac{-kx}{M+m}\)

on upper block \(F_{net} = ma\)

\(f= \frac{mk|x|}{M+m}\)

for maximum amplitude

\(f_{max} = \mu N = \frac{mkA_{max}}{M+m}\)

\(\mu mg = \frac{mkA_{max}}{M+m}\)

\(A_{max} = \frac{\mu(M+m)g}{k}\)