Question 15: Centre of Mass and Rotational Motion

Question

Which of the following graph shows the variation of velocity with mass for the constant momentum?
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lwm61qmr/476b1a8d-890e-4c2c-b88c-287e3286cc99/6f86d630-1a9d-11ef-9f0c-4b3df25a75e2/file-1lwm61qms.png?format=png)

Accepted Answer

When bob $A$ strikes to the bob $B$, then
$\begin{aligned}
m u & =(m+m) v^{\prime} \
\Rightarrow \quad v^{\prime} & =\frac{u}{2} \quad 	ext{.... (i)}
\end{aligned}$
The potential energy of $A$ at height $h$ gets converted into kinetic energy of this mass, at point $O$, i.e.
$\begin{aligned}
m g h & =\frac{1}{2} m u^2 \
\Rightarrow \quad u & =\sqrt{2 g h} \quad 	ext{[From Eq. (i)]}\
	herefore \quad v^{\prime} & =\frac{\sqrt{2 g h}}{2}=\sqrt{\frac{g h}{2}}
\end{aligned}$
Let the combined mass moves to a height $h^{\prime}$, then total mass $=2 m$
Then, $2 m g h^{\prime}=\frac{1}{2}(2 m) v^{\prime 2}$
$\Rightarrow \quad g h^{\prime}=\frac{g h}{4} \Rightarrow h^{\prime}=\frac{h}{4}$
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lqcifh17/a96f9107-e204-4d01-bcf9-98ef9aade9ba/b838dcb0-9e84-11ee-af68-2166ffe89748/file-6y3zli1lqcifh18.png?format=png)

Answer

Fig 3

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Fig 1

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Fig 2

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Fig 4

Centre of Mass and Rotational Motion

Which of the following graph shows the variation of velocity with mass for the constant momentum?

Choose the correct answer: