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When a force 1N acts on 1kg mass at rest for 1s, its final momentum is P. When 1N force acts on 1kg mass at rest through a distance 1m, its final momentum is $P^{|}$ . The ratio of P to $P^{|}$ is

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1 : 1

$1 : \sqrt{2}$

1 : 2

2 : 1

answer is B.

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Detailed Solution

$F = 1 N$

$P = F \times t = 1 k g m s^{- 1}$

$F = m a$

$1 = 1 \times a \Rightarrow a = 1 m s^{- 2}$

$P^{1} = m (\sqrt{2 a s}) = 1 \times \sqrt{2}$

$= \sqrt{2} k g m s^{- 1}$

$P : P^{1} = 1 : \sqrt{2}$

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