Conservation of linear momentum and impulse

A particle of mass m moving in the x-direction with speed 2 v

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Solving time: 3 mins

A particle of mass $m$ moving in the $x$ -direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ -direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
(a) $44%$
(b) $50%$
(c) $56%$
(d) $62%$

Views: 5,166 students

Updated on: Sep 11, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2015

Text solutionVerified

Exp. (c)
O Conservation of linear momentum can be applied but energy is not conserved.
Consider the movement of two particles as shown below.
Solution Image

Conserving linear momentum in

x

-direction

(p_{i}) x = (p_{f}) x or 2 m v = (2 m + m) v_{x}

v_{x} = \frac{2}{3} v

Conserving linear momentum in

y

-direction

(p_{i}) y = (p_{f}) y or 2 m v = (2 m + m) v_{y}

v_{y} = \frac{2}{3} v

Initial kinetic energy of the two particles system is

E_{i} = \frac{1}{2} m (2 v)^{2} + \frac{1}{2} (2 m) (v)^{2}

= \frac{1}{2} \times 4 m v^{2} + \frac{1}{2} \times 2 m v^{2}

= 2 m v^{2} + m v^{2} = 3 m v^{2}

Final energy of the combined two particles system is

E_{f} = \frac{1}{2} (3 m) (v_{x}^{2} + v_{y}^{2})

= \frac{1}{2} (3 m) [\frac{4 v ^{2}}{9} + \frac{4 v ^{2}}{9}] = \frac{3 m}{2} [\frac{8 v ^{2}}{9}] = \frac{4 m v ^{2}}{3}

Loss in the energy

Δ E = E_{i} - E_{f}

= m v^{2} [3 - \frac{4}{3}] = \frac{5}{3} m v^{2}

Percentage loss in the energy during the collision

\frac{Δ E}{E _{i}} \times 100 = \frac{( 5/3 ) m v ^{2}}{3 m v ^{2}} \times 100 = \frac{5}{9} \times 100 = 56%

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Eleanor Discussed

A particle of mass

m

moving in the

x

-direction with speed

2 v

is hit by another particle of mass

2 m

moving in the

y

-direction with speed

v

. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
(a)

44%

(b)

50%

(c)

56%

(d)

62%

14 mins ago

Discuss this question LIVE

14 mins ago

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Question Text	A particle of mass $m$ moving in the $x$ -direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ -direction with speed $v$ . If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to (a) $44%$ (b) $50%$ (c) $56%$ (d) $62%$
Updated On	Sep 11, 2023
Topic	Laws of motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 10
Upvotes	1012
Avg. Video Duration	8 min

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A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to(a) 44%(b) 50%(c) 56%(d) 62%

Text solutionVerified

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