Question

In the shown pulley-block system, strings are light. Pulleys are massless and smooth. System is released from rest. In $0.6$ second: [Take $g=10m/s^2$]

• A. Work done on $20kg$ block by gravity is $120J$
• B. Work done on $20kg$ block by string is $-20J$
• C. Work done on $10kg$ block by gravity is $-30J$
• D. Work done on $10kg$ block by string is $20J$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Work done on $20kg$ block by gravity is $120J$
B Work done on $10kg$ block by gravity is $-30J$
C Work done on $20kg$ block by string is $-20J$
D Work done on $10kg$ block by string is $20J$

$2T-10g=10a$ and $20g-T=40a$ $\Rightarrow$ $30g=90a$ $\Rightarrow$ $a=g/3$

For $\left(A\right):$ $W=mgh=\left(20\right)\left(10\right)[\frac{1}{2}\times \frac{g}{3}\times {\left(0.6\right)}^2]=120J$

For $\left(B\right):$ $T=\left(\frac{10g-10a}{2}\right)=\left(\frac{10g--10g/3}{2}\right)=\frac{10\left(\frac{2g}{3}\right)}{2}=\left(\frac{100}{3}\right)N$

$\Rightarrow W=-T\times \left(h\right)=-\frac{100}{3}\times \frac{6}{10}=-20J$

For $\left(C\right):$ $W_{gravity}=-mg\left(h/2\right)=-10\times \left(10\right)\left(\frac{6}{20}\right)=-30J$

For $\left(D\right):$ $=+20J$