Question

A constant force acts on a body of mass m at rest.The velocity v acquired in travelling 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

Answer: (B)

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

$F=ma$

$a=\frac{F}{m}$

also,$a=\frac{vdv}{dx}=\frac{F}{m}$.

Seperating the variables $dv$ and $dx$ and integrating both sides we get'

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

Since, only m and v are variable , we get the option $B$.