Q: Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a light and inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at 45° to the horizontal on both sides. The coefficient of friction between the block A and the wedge is 2/3 and that between the block B and the wedge is 1/3. If the system of A and B is released from rest, then the acceleration of A is

(a) 1.5 ms-2

(b) 0

(c) 0.5 ms-2

(d) 1 ms-2

Ans: (b)

(f_{max})_{A} = μ_{A}(m g cos45)

(f_{max})_{B} = μ_{B}(2m g cos45)

Hence , the maximum value of friction obtained is

f_{max} = (f_{max})_{A} + (f_{max})_{B} …(i)

Net pulling force on the system is

F = F_{1}-F_{2}

F = 2m g sin45 – mg sin45 …(ii)

Pulling force < f_{max}

Therefore, the system will not move or the acceleration of block A will be zero.