An explosion blows a rock into three parts Two parts go off at right angles to each other. These two are, $1…

An explosion blows a rock into three parts Two parts go off at right angles to each other. These two are, $1 \mathrm{~kg}$ first part moving with a velocity of $12 \mathrm{~ms}^{-1}$ and $2 \mathrm{~kg}$ second part moving with a velocity of $8 \mathrm{~ms}^{-1}$. If the thirds part files off with a velocity of $4 \mathrm{~ms}^{-1}$, its mass would be :
  1. $3 \mathrm{~kg}$
  2. $5 \mathrm{~kg}$
  3. $7 \mathrm{~kg}$
  4. $17 \mathrm{~kg}$

Solution

$\begin{aligned} \overrightarrow{\mathrm{P}}_1+\overrightarrow{\mathrm{P}}_2+\overrightarrow{\mathrm{P}}_3 & =0 \\ \left|\overrightarrow{\mathrm{P}}_3\right| & =\left|\overrightarrow{\mathrm{P}}_1+\overrightarrow{\mathrm{P}}_2\right| \\ \mathrm{m} \times 4 & =\sqrt{\mathrm{P}_1^2+\mathrm{P}_2^2} \\ & =\sqrt{12^2+16^2} \\ \mathrm{~m} & =5 \mathrm{~kg} \end{aligned}$

Asked in: NEET 2009 (Mains)

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