In the diagram shown, the block A and B are of the same mass M and the mass of the block C is `(M_(1))`. Friction is present only under the block A. the whole system is suddenly released from the state of rest. The minimum coefficient of friction on block A to keep it in the state of rest is equal to .

Options

A. (a) `(M_(1))/(M)`
B. (b) `(2M_(1))/(M)`
C. (c) `(M_(1))/(2M)`
D. (d) None of these`

Answer

B

Explanation

`Let X_(m)` is maximum elongation of spring. Then, incerase in potential energy of spring`=`decrease in potential energy of `C`.
`:. 1/2KX_(m)^(2) =M_(1)gX_(m)`
or `KX_(m) =`maximum spring force
`=2M_(1)g -mu_("min") Mg`
`:. mu_("min") =(2M_(1))/(M)`