Block A of mass m and block B of mass `2m` are placed on a fixed traingular wedge by means of a massless 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 blocks A and the wedge is `2//3` and that between block B and is released from rest find the following

The magnitude and direction of the force of friction acting on A are

Options

A. `mg` down the plane
B. `(mg)/(2)`up the plane
C. `(mg)/(sqrt(2))`,up the plane
D. `(mg)/(3sqrt(2))`down the plane

Answer

D

Explanation

`T = mg sin 45^(@) +f_(1) rArr f_(1) = (mg)/(3sqrt(2))`