MCQ
An artillery piece of mass $M_1$ fires a shell of mass $\mathrm{M}_2$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:
  • A
    $\mathrm{M}_1 /\left(\mathrm{M}_1+\mathrm{M}_2\right)$
  • $\frac{M_2}{M_1}$
  • C
    $\mathrm{M}_2 /\left(\mathrm{M}_1+\mathrm{M}_2\right)$
  • D
    $\frac{M_1}{M_2}$

Answer

Correct option: B.
$\frac{M_2}{M_1}$
b
$\left|\overrightarrow{\mathrm{p}_1}\right|=\left|\overrightarrow{\mathrm{p}_2}\right|$

$\mathrm{KE}=\frac{\mathrm{p}^2}{2 \mathrm{M}} ; \mathrm{p} \text { same }$

$\mathrm{KE} \propto \frac{1}{\mathrm{~m}}$

$\frac{\mathrm{KE}_1}{\mathrm{KE}_2}=\frac{\mathrm{p}^2 / 2 \mathrm{M}_1}{\mathrm{p}^2 / 2 \mathrm{M}_2}=\frac{\mathrm{M}_2}{\mathrm{M}_1}$

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