Question 261: Centre of Mass and Rotational Motion

Question

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ___________ ms$$^{-1}$$.

Accepted Answer

Before collision
After collision
Momentum conservation
u + 0 = 3 v Ã¢ÂÂ 2
3v - u = 2    Ã¢ÂÂ¦(1)
also,
$$
\begin{aligned}
& \frac{v+2}{u}=1 \Rightarrow v+2=u \\
& u-v=2 \quad ....(2)
\end{aligned}
$$
Adding (1) and (2)
$$
\begin{aligned}
& 2 v=4 \\
& v=2 \mathrm{~m} / \mathrm{s} \\
& 	herefore u=4 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$

Centre of Mass and Rotational Motion

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is ___________ ms$^{-1}$.

Integer / Numeric Answer Type