A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?
A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?
- A
$\frac{h}{e_1 + e_2}$
- B
$(e_1 + e_2)^2 \frac{h}{4}$
- C
$\frac{e_1^2 + e_2^2}{4}\times h$
- D
$\frac{4h}{e_1^2 + e_2^2}$
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Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : Body $'P'$ having mass $M$ moving with speed $'u'$ has head-on collision elastically with another body $'Q'$ having mass $'m'$ initially at rest. If $m< < M,$ body $'Q'$ will have a maximum speed equal to $'2u'$ after collision.
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In the light of the above statements, choose the most appropriate answer from the options given below:
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : Body $'P'$ having mass $M$ moving with speed $'u'$ has head-on collision elastically with another body $'Q'$ having mass $'m'$ initially at rest. If $m< < M,$ body $'Q'$ will have a maximum speed equal to $'2u'$ after collision.
Reason $R$ : During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below:
- [JEE MAIN 2021]