Question

In the pulley system shown in the figure, if radii of the bigger and smaller pulley are 2 m and 1 m respectively and the acceleration of block A is $5m/s^2$ in the downward direction, then the acceleration of block B will be

• A. $0m/s^2$
• B. $5m/s^2$
• C. $10m/s^2$
• D. $5/2m/s^2$

Answer 1

The correct option is D $5/2m/s^2$

Since both pulley are connected to each other.So, their angular acceleration are equal.

$\Rightarrow {\alpha }_1={\alpha }_2$

$\Rightarrow \frac{a_1}{r_1}$$=\frac{a_2}{r_2}$ because $\alpha =\frac{a}{r}$

$\Rightarrow \frac{a_1}{1}$$=\frac{5}{2}$ $(Given,a_2=5m/s^2)$

$\Rightarrow a_1=\frac{5}{2}m/s^2$

Therefore, D is correct option.