Neet Solved Paper 2015 Question 8
Question: 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
Options:
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}} $
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Answer:
Correct Answer: A
Solution:
As the machine delivers a constant power So F. v = constant = k (watts)
$ \Rightarrow ,m\frac{dv}{dt}.v=k $
$ \Rightarrow \int{vdv}=\frac{k}{m}\int{dt} $
$ \Rightarrow ,\frac{v^{2}}{2}=\frac{k}{m}t\Rightarrow c=\sqrt{\frac{2k}{m}t} $
Now force on the particle is given by $ F=m\frac{dv}{dt}=m\frac{d}{dt}{{( \frac{2kt}{m} )}^{\frac{1}{2}}} $
$ =\sqrt{2km}.,( \frac{1}{2}{t^{-\frac{1}{2}}} ) $ $ =\sqrt{\frac{mk}{2}}.{t^{-\frac{1}{2}}} $
