Question

In the pulley system shown. If radii of the bigger and smaller pulley are $2m$ and $1m$ 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. $5m/s^2$ upwards
• C. $10m/s^2$ upwards
• D. $5/2m/s^2$ upwards

Answer 1

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

w.r.t

$a=R\propto$

$a_1=R_1\propto$...........(1)

$a_2=R_2\propto$...........(2)

$a_1=2\alpha =5m/s^2$

using (1)

$2propto=5$

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

using (2)

$a_2=R_2\propto$

$a_2=1\times \frac{5}{2}$

$a_2=\frac{5}{2}m/s^{2}upwards$