Question

If mass of body is increased by 10 % and its speed is decreased by 10 % then percentage change
in magnitude of its momentum will be:
(A) 1 % increase (B) 1 % decrease (C) 2 % increase (D) 2 % decrease
​

Answer 1

Answer:

Let initial mass is m and initial speed is v...

Then initial momentum is m×v

If mass is increased by 10% then modified mass is 1.1×m.

If speed is decreased by 10% then modified speed is 0.9×v

Hence modified momentum is 1.1×m×0.9×v=0.99×m×v;

Hence momentum is decreased by 1%

Answer 2

Answer:

The percentage change in magnitude of its momentum will be a 1% decrease i.e.(B).

Explanation:

The momentum of a body is calculated as,

$P=mv$     (1)

Where,

P=momentum of the body

m=mass of the body

v=velocity with which the body is moving

As per the question,

The mass is increased by 10% so, m'=1.1m

The speed is decreased by 10% so, v'=0.9m

The new magnitude of momentum is given as,

$P'=m'v'$     (2)

By placing the values in equation (2) we get;

$P'=1.1m\times 0.9v$

$P'=0.99mv$    (3)

The percentage change in momentum is,

$\frac{P-P'}{P}\times 100$     (4)

By placing values in equation (4) we get;

$\frac{P-0.99P}{P}\times 100$

$0.01\times 100=1\%$

Hence, the percentage change in magnitude of its momentum will be a 1% decrease i.e.(B).

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