Question 115 of 130

A body of mass $2kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

A$1.8kg$B$1.2kg$C$1.0kg$D$1.5kg$

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Answer: (B) $1.2kg$

From conservation of linear momentum
$mU=m\dfrac{U}{4}+MV$ . . . (i)
For elastic collision: $e=1=\dfrac{V-\dfrac{U}{4}}{u}$
$V=\dfrac{5U}{4}$ . . . (ii)
From equation (i) & (ii),
$mU=m\dfrac{U}{4}+M\left(\dfrac{5U}{4}\right)$
$m=\dfrac{m}{4}+\dfrac{5}{4}M\Rightarrow M=\dfrac{3m}{5}=1.2kg$