An artillery piece of mass fires a shell of mass horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is

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Q.
An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

1 $\frac{M_{1}}{M_{1} + M_{2}}$

2 $\frac{M_{2}}{M_{1} + M_{2}}$

3 $\frac{M_{1}}{M_{2}}$

4 $\frac{M_{2}}{M_{1}}$

Ans.
(4)

$| \vec{p_{1}} | = | \vec{p_{2}} |$

$K E = \frac{p^{2}}{2 M} \Rightarrow$ $K E \propto \frac{1}{m}$

$\frac{K E_{1}}{K E_{2}} = \frac{p^{2} / 2 M_{1}}{p^{2} / 2 M_{2}} = \frac{M_{2}}{M_{1}}$

Solution

Q.
An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

1 $\frac{M_{1}}{M_{1} + M_{2}}$

2 $\frac{M_{2}}{M_{1} + M_{2}}$

3 $\frac{M_{1}}{M_{2}}$

4 $\frac{M_{2}}{M_{1}}$

Ans.
(4)

$| \vec{p_{1}} | = | \vec{p_{2}} |$

$K E = \frac{p^{2}}{2 M} \Rightarrow$ $K E \propto \frac{1}{m}$

$\frac{K E_{1}}{K E_{2}} = \frac{p^{2} / 2 M_{1}}{p^{2} / 2 M_{2}} = \frac{M_{2}}{M_{1}}$

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Solution

Q. An artillery piece of mass M1 fires a shell of mass M2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

1 M1M1+M2

2 M2M1+M2

3 M1M2

4 M2M1

Ans. (4) |p1→|=|p2→| KE=p22M⇒ KE∝1m KE1KE2=p2/2M1p2/2M2=M2M1

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Q.
An artillery piece of mass $M_{1}$ fires a shell of mass $M_{2}$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is [2024]

1 $\frac{M_{1}}{M_{1} + M_{2}}$

2 $\frac{M_{2}}{M_{1} + M_{2}}$

3 $\frac{M_{1}}{M_{2}}$

4 $\frac{M_{2}}{M_{1}}$

Ans.
(4)

$| \vec{p_{1}} | = | \vec{p_{2}} |$

$K E = \frac{p^{2}}{2 M} \Rightarrow$ $K E \propto \frac{1}{m}$

$\frac{K E_{1}}{K E_{2}} = \frac{p^{2} / 2 M_{1}}{p^{2} / 2 M_{2}} = \frac{M_{2}}{M_{1}}$