Question

A man is raising himself and the crate on which he stands with an acceleration of $5m/s^2$ by a massless rope and pulley arrangement. The mass of the man is 100 kg and that of the crate is 50 kg. If $g=10m/s^2$, then tension in the rope is

• A. 2250 N
• B. 1125 N
• C. 750 N
• D. 375 N

Answer 1

The correct option is B 1125 N


Let T be the tension in the string and a be the acceleration of the (man + crate) system.
Total mass of the system (man + crate) = (100 + 50)g = 150g
Free body diagram of the complete system (man + crate):
2T - 150g = 150a
$\Rightarrow 2T=150(a+g)=150(5+10)(\because a=5m/s^{2}andg=10m/s^2$
$\Rightarrow 2T=2250N$
$\Rightarrow T=1125N$
Hence, the correct answer is option (2).