JEE Advanced · Physics · 7. COM & Collisions
Three objects \(A, B\) and \(C\) are kept in a straight line on a frictionless horizontal surface. These have masses \(m, 2 m\) and \(m\), respectively. The object \(A\) moves towards \(B\) with a speed \(9 \mathrm{~ms}^{-1}\) and makes an elastic collision with it. Thereafter, \(B\) makes completely inelastic collision with \(C\). All motions occur on the same straight line. Find the final speed (in \(\mathrm{ms}^{-1}\) ) of the object \(C\).
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
After elastic collision,
\(
\begin{aligned}
v_A^{\prime} & =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\
& =-3 \mathrm{~ms}^{-1}
\end{aligned}
\)
Now from conservation of linear momentum after all collisions are complete,
\(m\left(+9 \mathrm{~ms}^{-1}\right) =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right)\)
\(\text { or } \quad v_C =4 \mathrm{~ms}^{-1}\)
\(
\begin{aligned}
v_A^{\prime} & =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\
& =-3 \mathrm{~ms}^{-1}
\end{aligned}
\)
Now from conservation of linear momentum after all collisions are complete,
\(m\left(+9 \mathrm{~ms}^{-1}\right) =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right)\)
\(\text { or } \quad v_C =4 \mathrm{~ms}^{-1}\)
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