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
53kgwt
B
103kgwt
C
6kgwt
D
3kgwt

Solution

## The correct option is B $$\dfrac{10}{3}kg\, wt$$$$\begin{array}{l} \text { The Reading of the } \\ \text { spring Balance is equal } \\ \text { to }(2 T) \text { where (T) } \\ \text { is the Tension in } \\ \text { the string. } \end{array}$$ $$\text {* FBD of } 5 \mathrm{~kg} \text { Block }$$ $$\begin{array}{l} \text { Let the Blocks move with } \\ \text { an acceleration a Downward. } \end{array}$$ $$\Rightarrow \quad 50-T=5 a \quad-0$$. $$\text { * FBD of Ikg Block }$$ $$\Rightarrow \quad T-10=1 \cdot a-(2)$$ $$\begin{array}{l} \text { On Solving eq }-(1) \text { and }(2) \\ \text { we get } T=\frac{50}{3} N=\frac{5 g}{3} N \end{array}$$ $$\begin{array}{l} \Rightarrow 2 T=\frac{\log N}{3} N \\ \text { Hence Reading of Spring Balance in } k g=\frac{10}{3} k g \end{array}$$Physics

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