Question

A particle of mass $m$ moves in circular path of radius $r$ with centripetal acceleration at any time $t$ is given as $a_c=kt$ then power of resultant force is:

• A. $\frac{mkr}{2}$
• B. $\frac{m\sqrt{kr}}{2}$
• C. $\frac{m{\left(kr\right)}^{\frac{3}{2}}}{2}$
• D. $\frac{kr}{2}$

Answer 1

The correct option is A $\frac{mkr}{2}$

Power = F.v

$a_c=kt$

$\frac{m{v}^2}{r}=kt$

$v=\sqrt{\frac{ktr}{m}}$

$\frac{dv}{dt}=\frac{1}{2\sqrt{\frac{ktr}{m}}}\sqrt{\frac{kr}{m}}$

$F=m\frac{dv}{dt}$

$=m\frac{1}{2\sqrt{\frac{ktr}{m}}}\sqrt{\frac{kr}{m}}$

$P=\frac{m}{2\sqrt{t}}$

$P=\frac{\sqrt{mkr}}{2V}$