Question

As situation shown in figure, choose the correct option(s) (take g = 10 $m/s^2$ downward).

• A. the acceleration of pulley is $\frac{5}{6}m/s^2$.
• B. the acceleration of pulley is $\frac{5}{12}m/s^2$.
• C. the acceleration of pulley is 0.
• D. tension in the string which connects the masses is 75 N.

Answer 1

The correct option is B the acceleration of pulley is $\frac{5}{12}m/s^2$.

Here $a_1,a_2$ are acceleration of blocks and T is tension and a is a acceleration of pulley.

$T-60=6a_2$ ...(1)

$90-T=9a_1$ ...(2)

2T = 150

T = 75

So $a_1=\frac{5}{2}m/se{c}^2$

$a_2=\frac{5}{2}m/se{c}^2$

So, acceleration of pulley

$a=\frac{a_2-a_1}{2}=\frac{\frac{5}{2}-\frac{5}{3}}{2}$

$=\frac{5}{12}m/se{c}^2$

Here option (B) is correct