Block of mass is placed on a rough plane inclined at to the horizontal

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Block

A

of mass

6\,\text{kg}

is placed on a rough plane inclined at

30^{\circ}

to the horizontal. The coefficient of static friction between

A

and the plane is

0.25

. A light inextensible string passes over a smooth pulley fixed at the top of the incline and carries block

B

of mass

m

hanging freely on the vertical side. The system is initially at rest. (i) Draw separate free-body diagrams for blocks

A

and

B

. (ii) Taking the possible tendency of motion of block

A

up the plane, write the equilibrium equations for the two blocks, clearly indicating the direction of the limiting friction acting on

A

. (iii) Hence obtain the range of values of

m

for which the system remains at rest without either block moving.