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प्रश्न
What happens to the kinetic energy when velocity of body is doubled at constant mass?
व्युत्पत्ती
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उत्तर
The kinetic energy increases by four times (becomes 4 times).
Mathematical Derivation:
Original Kinetic Energy:
\[ K = \frac{1}{2}mv^{2} \]
Substituting new velocity \(v' = 2v\) and keeping mass \(m' = m\):
\[ K' = \frac{1}{2}m(2v)^{2} \]
\[ = \frac{1}{2}m(4v^{2}) \]
\[ = 4 \times \left(\frac{1}{2}mv^{2}\right) \]
= 4 K
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