Question

A frictionless pulley of negligible weight is suspended from a spring balance. Masses of $1kg$ and $5kg$ are tied to the two ends of a string which passes over the pulley. The masses moves due to gravity. During motion, the reading of the spring balance will be

• A. $\frac{5}{3}kgwt$
• B. $\frac{10}{3}kgwt$
• C. $6kgwt$
• D. $3kgwt$

Answer 1

The correct option is B $\frac{10}{3}kgwt$

$\begin{array}{c}\text{The Reading of the}\\ \text{spring Balance is equal}\\ \text{to}\left(2T\right)\text{where (T)}\\ \text{is the Tension in}\\ \text{the string.}\end{array}$

$\text{* FBD of}5kg\text{Block}$

$\begin{array}{c}\text{Let the Blocks move with}\\ \text{an acceleration a Downward.}\end{array}$ $\Rightarrow 50-T=5a-0$.

$\text{* FBD of Ikg Block}$ $\Rightarrow T-10=1\cdot a-\left(2\right)$

$\begin{array}{c}\text{On Solving eq}-\left(1\right)\text{and}\left(2\right)\\ \text{we get}T=\frac{50}{3}N=\frac{5g}{3}N\end{array}$

$\begin{array}{c}\Rightarrow 2T=\frac{\log N}{3}N\\ \text{Hence Reading of Spring Balance in}kg=\frac{10}{3}kg\end{array}$