First slide

The steps in collision

Question

A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary
particle of mass m They are in contact for a brief time T. Their force of interaction increases from zero to F₀ linearly in time $\frac{T}{2}$ and decreases linearly to zero in further time $\frac{T}{2}$ . The magnitude of F₀ is.

Moderate

A

$\frac{m u}{T}$
B

$\frac{2 m u}{T}$
C

$\frac{m u}{2 T}$
D

None of these

Solution

In one dimensional elastic collision between two equal masses, their velocities are interchanged. Therefore, change in linear momentum of any of the particle will be mu.
Now, impulse or area under F-t graph gives the change in linear momentum.
$∴$ $\frac{1}{2} F_{0} T = mu$ or $F_{0} = \frac{2 mu}{T}$

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