Question 17: Centre of Mass and Rotational Motion

Question

Which of the following statement is true regarding the centre of mass of a system?

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

The centre of mass depends on the size and shape but does not depend on the distribution of mass of the body.

Answer

The centre of mass depends on the coordinate system.

Answer

The centre of mass of a system depends on the size and shape of the body but independent of the co-ordinate system

Answer

The centre of mass of a body always lies inside the body.

Centre of Mass and Rotational Motion

Which of the following statement is true regarding the centre of mass of a system?

Choose the correct answer: