Question

In the given figure, the pulleys and the string are light. $T$ is the tension in the string. Taking $g=10m{s}^{-2}$, which of the following is correct?

• A. The acceleration of the system is $5m{s}^{-2}$
• B. The acceleration of the system is $10m{s}^{-2}$
• C. $T=0N$
• D. $T=15N$

Answer 1

Answer: (A)

The acceleration of the system is $5m{s}^{-2}$

Refer to free body diagram of hanging mass.
$g-T=a....\left(i\right)$
Again, refer to the free body diagram of the mass on horizontal surface.
$T=a....\left(ii\right)$
Adding (i) and (ii),
$g=2a$
or $a=\frac{g}{2}m{s}^{-2}=5m{s}^{-2}$
From equation (ii), $T=5N$, Hence (a) is correct.