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Q.

The linear momentum p of a body moving in one dimension varies with time according to the equating $P = a + b t^{2}$ where a and b are positive constants. The net force acting on the body is

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a

Proportional to $t^{2}$

b

A constant

c

Proportional to t

d

Inversely proportional to t

answer is C.

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Detailed Solution

Linear momentum, $P = a + b t^{2}$

$\frac{d P}{d t} = 2 b t$ (on differentiation)

F= 2 b t

$∴$ Rate of change of momentum, $\frac{d p}{d t} α F$

By 2nd law of motion, $\frac{d P}{d t} \propto F$

$∴ F \propto t$

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