Question

A constant force acts on a body of mass m at rest. The velocity V acquired in traversing a specific distance depends on m as

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

Answer 1

The correct option is B $V\propto \frac{1}{\sqrt{m}}$

By Newton's second law,

$F=ma$

$a=\frac{F}{m}=\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=v.\frac{dv}{dx}$

Thus,

$\frac{Fdx}{m}=v.dv$

Integrating we get

$\frac{Fx}{m}=\frac{v^2}{2}+c$

we get $c=0$ by substituting $v=0$ at $x=0$.

$\frac{Fx}{m}=\frac{v^2}{2}$

so,

$v\alpha \frac{1}{\sqrt{m}}$