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?

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, $$2 m g h^{\prime}=\frac{1}{2}(2 m) v^{\prime 2}$$
$$\Rightarrow \quad g h^{\prime}=\frac{g h}{4} \Rightarrow h^{\prime}=\frac{h}{4}$$

Answer

Fig 3

Answer

Fig 1

Answer

Fig 2

Answer

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: