Question

In the given arrangement of a doubly inclined plane, two blocks of masses \( M \) and \( m \) are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of \( m \), for which \( M = 10 \, \text{kg} \) will move down with an acceleration of \( 2 \, \text{m/s}^2 \), is: (take \( g = 10 \, \text{m/s}^2 \) and \( \tan 37^\circ = 3/4 \))

• A. 9 kg
• B. 4.5 kg
• C. 6.5 kg
• D. 2.25 kg

Answer 1

The Correct Option is B

Considering the forces acting on block \( M \) on the inclined plane:

\[ 10g \sin 53^\circ - \mu (10g) \cos 53^\circ - T = 10 \times 2 \]

Substituting values:

\[ T = 80 - 15 - 20 = 45 \, \text{N} \]

For block \( m \) on the other inclined plane:

\[ T - mg \sin 37^\circ - \mu mg \cos 37^\circ = m \times 2 \]

Substituting values:

\[ 45 = 10m \] \[ m = 4.5 \, \text{kg} \]