First slide

Kinetic energy

Question

If $ν, ρ$ and E denote velocity, linear momentum and kinetic energy of the particle respectively, then

Easy

A

$p = \frac{d E}{d v}$
B

$p = \frac{d E}{d t}$
C

$p = \frac{d v}{d t}$
D

$p = \frac{d E}{d v} \times \frac{d E}{d t}$

Solution

Kinetic energy, $E = \frac{1}{2} m v^{2}$
$∴ \frac{d E}{d v} = m v or p = \frac{d E}{d v}$ $(∵ m v = p)$

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