Question

Under the application of a constant force, starting from rest and moving for some fixed distance, the kinetic energy of a mass m is proportional to:

• A. $\sqrt{m}$
• B. Does not depend on m
• C. $1/\sqrt{m}$
• D. m

Answer 1

The correct option is B Does not depend on m

work done on a body is $W=F.s$
Irrespective of the mass the increase in KE will be equal to work done on the body by conservation of energy principle.
$\therefore$ KE will not depend on m for the given case.

OR

F = constant = ma

$⟹a=F/m$ .......... (1)

Now from the third equation of motion, $v^2=u^2+2as$

Since started from rest, u = 0,

$v^2=2as$

$v^2=2\times \frac{F}{m}\times s$ ..........from (1)

$\frac{1}{2}m{v}^2=Fs$

$K.E.=Fs$ ............. (2)

So, from (2), we can say that Kinetic Energy is independent of mass.