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The linear momentum P of a particle varies with the time as follows $P = a + {bt}^{2}$ . Where a and b are constants. The net force acting on the particle is

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Proportional to t

Proportional to t²

Constant

Zero

answer is A.

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Detailed Solution

$P = a + {bt}^{2}$

$\begin{matrix} \frac{dP}{dt} = \frac{d}{dt} (a + {bt}^{2}) \\ = \frac{d}{dt} a + \frac{d}{dt} {bt}^{2} \\ = 0 + b 2 t \\ F = 2 bt \\ F \propto t \end{matrix}$

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