The kinetic energy of a body is increased by 4 times. Its momentum will
The kinetic energy of a body is increased by 4 times. Its momentum will
- increase twice
- increase four times
- decrease twice
- remains constant
Solution
Given, initial kinetic energy, \(K_1=K\)
Final kinetic energy, \(K_2=4 K\)
Momentum and kinetic energy are related as,
\(\begin{aligned}
& \qquad K=\frac{p^2}{2 m} \Rightarrow p=\sqrt{2 m K} \\
& \begin{aligned}
\therefore \text {Initial momentum, } p_1 & =\sqrt{2 m K_1} \\
\Rightarrow & =\sqrt{2 m K} \quad \ldots (i) \\
\text {Final momentum, } p_2 & =\sqrt{2 m K_2}=\sqrt{2 m \cdot 4 K} \\
\Rightarrow & \ldots \text { (i) } \\
& =2 \sqrt{2 m K}=2 p_1 \quad \text { [from Eq. (i)] }
\end{aligned}
\end{aligned}\)
Asked in: AP EAMCET 2020 (18 Sep Shift 2)
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