A particle moves in the $x$-$y$ plane under the action of a force $F$ such that the value of its linear momentum $\overrightarrow{P}\ $at any time $t$ is $p_{x} = 2$ cos $t,p_{y}2\sin t$ The angel $ heta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be

Question

A particle moves in the $x$-$y$ plane under the action of a force $F$ such that the value of its linear momentum $\overrightarrow{P}\ $at any time $t$ is $p_{x} = 2$ cos $t,p_{y}2\sin t$ The angel $	heta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be

Dr. Abubacker · Accepted Answer

(a) $P = \sqrt{p_{x}^{2} + p_{y}^{2}}$
$= \sqrt{\left( 2\cos t ight)^{2} + \left( 2\sin t ight)^{2}} = 2$
If $m$ be the mass of the body, then kinetic energy
$= \frac{p^{2}}{2m} = \frac{(2)^{2}}{2m} = \frac{2}{m}$
Since kinetic energy does not change with time, both work done and power are zero
Now Power = $Fv\cos{	heta = 0}$
As $F 
eq 0,v 
eq 0$
$	herefore\ \cos{	heta = 0}$
Or $	heta = 90{^\circ}$
As direction of $\overrightarrow{p}$ is same that $\overrightarrow{v}(\because\overrightarrow{p} = m\overrightarrow{v})$ hence angle between $\overrightarrow{F}$ and $\overrightarrow{p}$ is equal to $90{^\circ}$

Q. A particle moves in the $x$-$y$ plane under the action of a force $F$ such that the value of its linear momentum $\overrightarrow{P}\ $at any time $t$ is $p_{x} = 2$ cos $t,p_{y}2\sin t$ The angel $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be

Explanation

Reviewed by Dr. Abubacker

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