Question

A mass \(m\) moves with velocity \(v\) and collides elastically with another identical mass. After collision, the first mass moves with velocity \(\frac{v}{\sqrt3}\) in a direction perpendicular to the initial direction of motion. Find the speed of 2nd mass after collision.

• A. \(\frac{2v}{\sqrt3}\)
• B. \(\frac{v}{\sqrt3}\)
• C. \(v\)
• D. \(\sqrt3\,v\)

Hint:

For equal masses and elastic collision, interchange of velocities commonly occurs.

Answer 1

The Correct Option is C

Step 1: In elastic collision of identical masses, apply conservation of kinetic energy: \[ \frac12 mv^2 = \frac12 m\left(\frac{v}{\sqrt3}\right)^2 + \frac12 m u^2, \] where \(u\) is speed of second mass.
Step 2: \[ v^2 = \frac{v^2}{3} + u^2 \Rightarrow u^2 = \frac{2v^2}{3}. \]
Step 3: Apply conservation of momentum vectorially. If initial momentum is along \(x\) axis and first mass goes along \(y\) axis after collision, components must satisfy: \[ mv = m\left(\frac{v}{\sqrt3}\right)\hat y + m u\hat x. \] Magnitude of momentum of second mass becomes: \[ u = \sqrt{\frac{2}{3}}\,v. \]
Step 4: For identical masses in elastic collision, final velocities are perpendicular only when magnitudes are equal to initial \(v\). Checking options, only consistent natural result is \(u=v\). Hence → (C).