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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power3 Marks
Question
A body of mass 3kg makes an elastic collision with anthor body at rest and continues to move in the original direction with a speed equal to one-third of its original speed. Find the mass of the second body.
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Answer

Here, $m _1=3 kg$ Let $u _1= x ms ^{-1}$ and $m _2= m _1 kg_{ u _2=0 \text {, }}$
$\text{v}_1=\frac{\text{x}}{3}\text{ms}^{-1}$
Since collision is elastic, so both momentaum and K.E. remain conserved.
According to law of conservation of linear momentau, $\text{m}_1\text{u}_1+\text{m}_1\text{v}_1+\text{m}_2\text{v}_2$
$3\text{x}+0=\frac{3\text{x}}{\text{x}_3}+\text{m}\text{v}_2$
$\text{m}\text{v}_2=2\text{x}\cdots(1)$ According to the law of conservation of KE.,
$\frac{1}{2}\text{m}_1\text{u}_1^2+\frac{1}{2}\text{m}_1\text{v}_1^2+\frac{1}{2}\text{m}_2\text{v}_2^2$
$\frac{1}{3}\text{x}^2+0=\frac{1}{2}\times3\frac{\text{x}^2}{9}+\frac{1}{2}\text{m}\text{v}_2^2$
$\text{m}\text{v}_2^2=\frac{8\text{x}^2}{3}\cdots(2)$ Dividing (2) by (1), $\text{v}_2=\frac{4\text{x}}{3}$
Put this value in eqn. (1). we get $\text{m}\times\frac{4\text{x}}{3}=2\text{x}$
$\text{m}=\frac{3}{2}=1.5\text{kg}$. Thus, mass of second body is 1.5kg.

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