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Linear momentum of particle is increased by (a) 100 % (b) 1 %

Question

Medium

Solving time: 3 mins

Linear momentum of particle is increased by
(a) $100%$
(b) $1%$
without changing its mass. Find percentage increase in its kinetic energy in both cases.

Views: 5,515 students

Book:

Mechanics Volume 2 (DC Pandey)

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James Discussed

Linear momentum of particle is increased by
(a)

100%

(b)

1%

without changing its mass. Find percentage increase in its kinetic energy in both cases.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

(a) Relation between kinetic energy

K

and momentum

p

is given by:

K = \frac{p ^{2}}{2 m}

... (i)

Now, momentum is increased by

100%

.
So, new momentum,

p^{'} = 2 p

K^{'} = \frac{( p ^{'} ) ^{2}}{2 m} = \frac{( 2 p ) ^{2}}{2 m} = 4 [\frac{p ^{2}}{2 m}] = 4 K

[From Eq. (i)]
Now percentage change in kinetic energy,

= (\frac{Final value - Initial value}{Initial value}) \times 100 = (\frac{K ^{'} - K}{K}) \times 100 = (\frac{4 K - K}{K}) \times 100 = + 300%

Ans.
Plus sign indicates that, with increase in linear momentum, kinetic energy will also increase.
(b)

K = \frac{p ^{2}}{2 m}

K \propto p^{2}

(as

m =

constant)
Here, power of

K

is 1 and power of

p

is 2 . For small changes, we can write it like this (1)

(%

change in

K) = (2) (%

change in

p)

%

change in

K = (2) (1%) = + 2%

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Question Text	Linear momentum of particle is increased by (a) $100%$ (b) $1%$ without changing its mass. Find percentage increase in its kinetic energy in both cases.
Topic	Laws of motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	139

Linear momentum of particle is increased by
(a) $100%$
(b) $1%$
without changing its mass. Find percentage increase in its kinetic energy in both cases.

Text solutionVerified

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Linear momentum of particle is increased by
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