Question

A constant force ($F$) is applied on a stationary particle of mass $m$. The velocity attained by the particle in a certain displacement will be proportional to:

• A. $m$
• B. $1/m$
• C. $\sqrt{m}$
• D. $\frac{1}{\sqrt{m}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{m}}$

We know,
$F=ma$
$a=\frac{F}{m}$
Moreover,
$v^2=u^2+2aS$
$\Rightarrow v^2=2\times \frac{F}{m}\times S$
$v=\sqrt{2\times \frac{F}{m}\times S}$
$\Rightarrow v\propto \frac{1}{\sqrt{m}}$