JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Conservation of Momentum

A particle of mass

m

is moving in a straight line with momentum

p

. Starting at time

t = 0

, a force

F = k t

acts in the same direction on the moving particle during time interval

T

so that its momentum changes from

p

3 p

. Here

k

is a constant. The value of

T

is:

(A) $2 \frac{k}{p}$
(B) $2 \frac{p}{k}$ ✓ Correct
(C) $\frac{2 k}{p}$
(D) $\frac{2 p}{k}$

Answer: (B)

Solution

The applied force equals the rate of change of momentum,

\frac{d p}{d t} = k t

. Integrating as the momentum grows from

p

3 p

while time runs from

0

T

\int_{p}^{3 p} d p = \int_{0}^{T} k t d t

, so

2 p = \frac{k T ^{2}}{2}

. Hence

T^{2} = \frac{4 p}{k}

and

T = 2 \frac{p}{k}

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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