Question

A force $\overrightarrow{F}=(2t\hat{i}+3t^2\hat{j})N$ acts on an object moving in xy plane. Find magnitude of change momentum of the object in time interval $t=0$ to $t=2$s.

• A. $\sqrt{8}$
• B. $7$
• C. $\sqrt{80}$
• D. $\sqrt{56}$

Answer 1

The correct option is C $\sqrt{80}$

$F-\frac{dp}{dt}$

$P={\int }_0^{2}f.dt$

$P={\int }_0^2(2t\hat{i}+3t^2\hat{j})$

$P=t^2\hat{i}+t^3\hat{j}\int$

$P=4\hat{i}+8\hat{j}$

$P=\sqrt{64+16}$

$P=\sqrt{80}$