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:

  1. (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} $