Question

A particle of mass $m$ is lying on a smooth horizontal surface. A tangential force $F$ is applied to it, then instantaneous power delivered to the particle is

• A. $\frac{F^{2}t}{m}$
• B. $\frac{F^{2}t}{2m}$
• C. $\frac{Ft}{m}$
• D. $\frac{Ft}{2m}$

Answer 1

The correct option is A $\frac{F^{2}t}{m}$

Given:
Mass of particle $=m$
Force applied to it $=F$

So, acceleration of particle,
$a=\frac{F}{m}=$ constant
Now, velocity,
$v=at=\frac{Ft}{m}$ ..............(1)
We know power of a force is given by,
$P=\overrightarrow{F}.\overrightarrow{v}$, where $\overrightarrow{F}$ is force applied and $\overrightarrow{v}$ is velocity of block.
$\Rightarrow P=Fv\cos \theta$
$\Rightarrow P=Fv\cos 0^{\circ }$
[ particle is at rest and will start moving in direction of force ]
$\Rightarrow P=Fv$
$\Rightarrow P=F\times \frac{Ft}{m}$
[ from (1) ]
$\Rightarrow P=\frac{F^{2}t}{m}$
Hence option $\left(a\right)$ is correct.