A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $\mathrm{v}=\alpha \sqrt{\mathrm{x}}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{d}$, will be:
A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $\mathrm{v}=\alpha \sqrt{\mathrm{x}}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{d}$, will be:
- [JEE MAIN 2024]
- A
$\frac{\mathrm{m}}{2 \alpha^2 \mathrm{~d}}$
- B
$\frac{\mathrm{md}}{2 \alpha^2}$
- C
$\frac{m \alpha^2 d}{2}$
- D
$2 m \alpha^2 d$
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- [JEE MAIN 2021]
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- [AIEEE 2005]