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

Answer: (B)

4.5 kg

Answer 2

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:

$45 = 10m$ $m = 4.5 \, \text{kg}$