Question

Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are smooth.
$\left(i\right)$ Find the acceleration of $1kg$ block.
$\left(ii\right)$Find the tension in the string. $(g=10m/s^2)$

Answer 1

Consider the acceleration of mass $1kg$ be $a$ and the acceleration of mass $2kg$ be $\frac{a}{2}$

$\left(i\right)$

$\begin{array}{c}2\times \frac{a}{2}-2T=0\\ \Rightarrow a-2T=0\end{array}$

Again,

$\begin{array}{c}T+\left(1\times a\right)-\left(1\times g\right)=0\\ \Rightarrow \frac{a}{2}+a-g=0\\ \Rightarrow 3a=2g\\ \Rightarrow a=\frac{2g}{3}=6.67m/s^2\end{array}$

Therefore, the acceleration of $1kg$ block is $6.67m/s^2$

$\left(ii\right)$

$\begin{array}{c}T=\frac{a}{2}\\ =\frac{6.67}{2}\\ =3.33N\end{array}$

Hence, tension in the string is $3.33N$