Question

The force f is acting on a body varies with its displacement x as f=kx ^-2/3. The power delivered by the force will be proportional to

Answer 1

$P\propto x^{\frac{1}{3} }$ power is proportional to the cube root of displacement.

Explanation:

Since force on a body is a function of displacement given as:

$F=k.x^{-\frac{2}{3} }$

Then the work done is given by:

$W=F.x$

$W=k.x^{\frac{1}{3} }$

As we know that power is the rate of doing work and mathematically given as:

$P=\frac{W}{t}$

$P=\frac{k.x^{\frac{1}{3} }}{t}$

Therefore,

$P\propto x^{\frac{1}{3} }$

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TOPIC: power

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