A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√(x), where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be: (a) (m)/(2α² d) (b) (md)/(2α²) (c) (mα² d)/(2) (d) 2mα² d

Answer: (c). Total work = change in KE. v(0) = 0, v(d) = α√(d) ⇒ v² = α² d W = 1/2mα² d So the answer is (c) (mα² d)/(2).

A particle of mass m moves on a straight line with its velocity… | JEE Main 2024 (9 Apr, Shift 1)

Q7JEE Main 2024 · 9 APR · SHIFT 1Medium

Work-Energy Theorem

A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v = \alpha\sqrt{x}$ , where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x = 0$ to $x = d$ , will be:

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Answer: (c)

Total work $=$ change in KE.
$v(0) = 0$ , $v(d) = \alpha\sqrt{d} \Rightarrow v^2 = \alpha^2 d$
$W = \frac{1}{2}m\alpha^2 d$
So the answer is (c) $\frac{m\alpha^2 d}{2}$ .

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