Question 35: Centre of Mass and Rotational Motion

Question

A body of mass 1000 kg is moving horizontally
with a velocity 50 m/s. A mass of 250 kg is
added. Find the final velocity.

Accepted Answer

Mass of the body, $$m=1000 \mathrm{~kg}$$
$$v=50 \mathrm{~m} / \mathrm{s}$$
After adding $$250 \mathrm{~kg}$$, new mass of the body,
$$\begin{aligned}m^{\prime} & =m+250 \
& =1000+250 \
& =1250 \mathrm{~kg}
\end{aligned}$$
If $$v'$$ be the final velocity of the body, then by conservation of linear momentum,
$$\begin{aligned}m v & =m^{\prime} v^{\prime} \
\Rightarrow 1000 	imes 50 & =1250 	imes v^{\prime} \
\Rightarrow \quad v^{\prime} & =\frac{1000 	imes 50}{1250} \
& =40 \mathrm{~m} / \mathrm{s}
\end{aligned}$$

Answer

40 m/s

Answer

20 m/s

Answer

30$$\sqrt2$$ m/s

Answer

50 m/s

Centre of Mass and Rotational Motion

A body of mass 1000 kg is moving horizontally with a velocity 50 m/s. A mass of 250 kg is added. Find the final velocity.

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