Q14 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Work Power Energy

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:

Correct answer
A
$\sqrt{\frac{m k}{2}} t^{- \frac{1}{2}}$
B
$\sqrt{m k} t^{- \frac{1}{2}}$
C
$\sqrt{2 m k} t^{- \frac{1}{2}}$
D
$\frac{1}{2} \sqrt{m k} t^{- \frac{1}{2}}$

Solution

F v = c o n s t a n t = k

\frac{m d v}{d t} v = k

\int v d v = \int \frac{k}{m} d t

\frac{v^{2}}{2} = \frac{k}{m} t

v = \sqrt{\frac{2 k}{m} t}

F = \frac{m d v}{d t}

= m \sqrt{\frac{2 k}{m}} \frac{1}{2} t^{- \frac{1}{2}}

= \sqrt{\frac{m k}{2}} t^{- \frac{1}{2}}

Hence, the correct answer is option: 'A'.

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