Work Energy and Power - Result Question 34
37. A particle of mass $m$ is driven by a machine that delivers a constant power of $k$ watts. If the particle starts from rest the force on the particle at time $t$ is
[2015]
(a) $\sqrt{mk} t^{-1 / 2}$
(b) $\sqrt{2 mk} t^{-1 / 2}$
(c) $\frac{1}{2} \sqrt{mk} t^{-1 / 2}$
(d) $\sqrt{\frac{mk}{2}} t^{-1 / 2}$
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Answer:
Correct Answer: 37. (d)
Solution:
- (d) As we know power $P=\frac{d w}{d t}$
$\Rightarrow \quad w=P t=\frac{1}{2} mV^{2}$
So, $v=\sqrt{\frac{2 Pt}{m}}$ Hence, acceleration $a=\frac{d V}{d t}=\sqrt{\frac{2 P}{m}} \cdot \frac{1}{2 \sqrt{t}}$
Therefore, force on the particle at time ’ $t$ '
$ =m a=\sqrt{\frac{2 K m^{2}}{m}} \cdot \frac{1}{2 \sqrt{t}}=\sqrt{\frac{K m}{2 t}}=\sqrt{\frac{m K}{2}} t^{-1 / 2} $
