First slide

Types of collision

Question

A dumbell 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 coefficients of restitution are e₁ and e₂ (e₁< e₂). To what maximum height will the centre of mass of the dumbell rise after bouncing off the pads?

Easy

A

$\large \frac{h}{{{e_1} + {e_2}}}$
B

$\large {({e_1} + {e_2})^2}\frac{h}{4}$
C

$\large \frac{{e_1^2 + e_2^2}}{4}$
D

$\large \frac{{4h}}{{e_1^2 + e_2^2}}$

Solution

The centre of mass of the system after collision will move up with velocity at
$\large \frac{{({e_1} + {e_2})\sqrt {2gh} }}{2}$
$\large \Rightarrow \;0 = {\left[ {\frac{{({e_1} + {e_2})}}{2}\sqrt {2gh} } \right]^2} - 2gh'$
$\large h^{'}=\frac{{({e_1+e_2})^2}h}{{4}}$
Hence, (2) is the correct choice

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