Question

Consider the situation shown in figure (5 - E9). All the surface are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

• A. g / 5 m/ s${}^2$
• B. g / 8 m/ s${}^2$
• C. g / 10 m/ s${}^2$
• D. g /9 m/ s${}^2$

Answer 1

The correct option is C g / 10 m/ s${}^2$

Given :

Mass of each block is $1kg$

$sin{\theta }_1=\frac{4}{5}$

$sin{\theta }_2=\frac{3}{5}$.

The free-body diagrams for both the boxes are shown below:

$mgsin{\theta }_1-T=ma$ …(i)

$T-mgsin{\theta }_2=ma$ …(ii)

Adding equations (i) and (ii), we get:

$mg(sin{\theta }_1-sin{\theta }_2)=2ma$

$⟹2a=g(sin{\theta }_1-sin{\theta }_2)$

$⟹a=\frac{g}{5}\times \frac{1}{2}$

$=\frac{g}{10}m/s^2$