Question

Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are smooth. Find the tension in the string. ($g=10m/s^2$)

• A. $\frac{10}{3}N$
• B. $10N$
• C. $5N$
• D. $20N$

Answer 1

The correct option is A $\frac{10}{3}N$

Let the displacement of blocks of mass $1kg$ and $2kg$ be $x_1$ and $x_2$ respectively.

Using work theorem : $2T{x}_2-T{x}_1=0$

$\therefore$ $x_1=2x_2$

Differentiating twice w.r.t time we get, $2a_2=a_1$ $⟹a_2=\frac{a}{2}$

For block of mass $2kg$ : $2\left(a/2\right)=2T$ $⟹a=2T$ .........(1)

For block of mass $1kg$ : $a=g-T$

$\therefore$ $a=g-\frac{a}{2}$ $⟹a=\frac{2g}{3}$

$⟹$ Tension $T=\frac{g}{3}=\frac{10}{3}N$ (from 1)