A block B is placed over a cart which in turn lies over a smooth horizontal floor. Block A and Block C are connected to block B with light inextensible strings passing over light frictionless pulleys fixed to the cart as shown. Initially the blocks and the cart are at rest. All the three blocks have mass m and the cart has mass `M(M=3m)`. Now a constant horizontal force of magnitude F is applied to block A towards right.
Q. Let the coefficient of friction between block B and cart is `mu(mugt0)` and friction is absent everywhere else. Then the maximum value of force F applied to block A such that there is no relative acceleration between block B and cart is

Options

A. `mumg`
B. `2mumg`
C. `3mumg`
D. `4mumg`

Answer

B

Explanation

For block B to just slip on the cart, the friction force on cart is `mumg`. The net force on cart is thus `mumg`. Hence acceleratoin of cart is `a=(mumg)/(3m)=(mug)/(3)`