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A body of mass $2 \; kg$ 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 ?

Option 1)
$1.0 \: kg$

Option 2)
$1.5\: kg$

Option 3)
$1.8\: kg$

Option 4)
$1.2 \: kg$

Answers (1)

best_answer

$m\Rightarrow$ mass of $A$ body = $2kg$

$u\Rightarrow$ initial velocity of $A$ body

$M\Rightarrow$ mass of $B$ body

A B

$m\rightarrow u$ $M\Rightarrow$ $m\rightarrow \frac{u}{4}$ $M\rightarrow V$

rest

$V-\frac{u}{4}=u$ (from e=1)

$\Rightarrow V=\frac{5u}{4}$

momentum balance

$mu=\frac{mu}{4}+MV$

$\Rightarrow \frac{3mu}{4}=M\left ( \frac{5u}{4} \right )$

$\Rightarrow M=\frac{3m}{5}$

$=\frac{3\times 2}{5}$

$M=\frac{6}{5}kg$

$=1.2\; kg$

Option 1)

$1.0 \: kg$

Option 2)

$1.5\: kg$

Option 3)

$1.8\: kg$

Option 4)

$1.2 \: kg$

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