A trolley of mass 5 ,kg on a horizontal smooth surface is pulled … - Vidyadip

MCQ

A trolley of mass $5\,kg$ on a horizontal smooth surface is pulled by a load of mass $2\,kg$ by means of uniform rope $ABC$ of length $2\,m$ and mass $ 1\,kg.$ As the load falls from $BC = 0$ to $BC = 2\,m,$ its acceleration in $m/s^2$ changes from

A
$\frac{{20}}{6}$ to $\frac{{20}}{5}$
✓
$\frac{{20}}{8}$ to $\frac{{30}}{8}$
C
$\frac{{20}}{5}$ to $\frac{{30}}{6}$
D
None of the above

✓

Answer

Correct option: B.

$\frac{{20}}{8}$ to $\frac{{30}}{8}$

b
For $\quad \mathrm{BC}=0, \mathrm{a}=\frac{2 \mathrm{g}}{2+5+1}=\frac{\mathrm{g}}{4}=\frac{10}{4}=\frac{20}{8} \mathrm{ms}^{-2}$
For $\quad \mathrm{BC}=2 \mathrm{m}, \mathrm{a}=\frac{(2+1) \mathrm{g}}{2+5+1}=\frac{3 \mathrm{g}}{8}=\frac{30}{8} \mathrm{ms}^{-2}$

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