Looking for classes? Ksquare Career Institute, Bengaluru →
A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is
A
$\sqrt{\frac{mk}{2}}\,t^{-1/2}$
B
$\sqrt{mk}\,t^{-1/2}$
C
$\sqrt{2mk}\,t^{-1/2}$
D
$\frac{1}{2}\sqrt{mk}\,t^{-1/2}$
Detailed Solution
Work done in time t: $W = Pt = kt$
By the work-energy theorem, $\frac{1}{2}mv^2 = kt \Rightarrow v = \sqrt{\frac{2kt}{m}}$
$P = Fv \Rightarrow F = \frac{k}{v} = k\sqrt{\frac{m}{2kt}} = \sqrt{\frac{mk}{2t}}$
$F = \sqrt{\frac{mk}{2}}\,t^{-1/2}$
By the work-energy theorem, $\frac{1}{2}mv^2 = kt \Rightarrow v = \sqrt{\frac{2kt}{m}}$
$P = Fv \Rightarrow F = \frac{k}{v} = k\sqrt{\frac{m}{2kt}} = \sqrt{\frac{mk}{2t}}$
$F = \sqrt{\frac{mk}{2}}\,t^{-1/2}$