(D) According to the work-energy theorem,the work done $(W)$ on a particle is equal to the change in its kinetic energy.Since the particle is initiall

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(D) According to the work-energy theorem,the work done $(W)$ on a particle is equal to the change in its kinetic energy.Since the particle is initially at rest,its initial kinetic energy is $0$.Therefore,$W = K_f - K_i = \frac{1}{2}mv^2 - 0 = \frac{1}{2}mv^2$.Here,$m$ is the mass of the particle,which is constant.Thus,$W \propto v^2$.This relationship represents a parabola opening along the $W$-axis.Therefore,the graph between $W$ and $v$ will be parabolic in nature,as shown in option $(D)$.

Class 11 Physics Work, Energy, Power and Collision Work Energy Theorem and Conservation of Mechanical Energy

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$A$ particle,initially at rest on a frictionless horizontal surface,is acted upon by a horizontal force which is constant in size and direction. $A$ graph is plotted between the work done $(W)$ on the particle and the speed of the particle $(v)$. If there are no other horizontal forces acting on the particle,the graph would look like:

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Work, Energy, Power and Collision

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Work Energy Theorem and Conservation of Mechanical Energy

The total work done on a particle is equal to the change in its kinetic energy. This is applicable:

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The rain drop of mass $1 \text{ g}$,starts with zero velocity from a height of $1 \text{ km}$. It hits the ground with a speed of $5 \text{ m/s}$. The work done by the unknown resistive force is . . . . . . $J$. (take $g = 10 \text{ m/s}^2$)

DifficultJEE MAIN 2026

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$A$ bullet of mass $10 \; g$ leaves a rifle at an initial velocity of $1000 \; m/s$ and strikes the earth at the same level with a velocity of $500 \; m/s$. The work done in joule $(J)$ in overcoming the resistance of air will be:

MediumAIPMT 1989

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$A$ 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:

DifficultJEE MAIN 2024

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The average force necessary to stop a bullet of mass $20\, g$ moving with a speed of $250\, m/s$,as it penetrates into the wood for a distance of $12\, cm$ is

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The total work done on a particle is equal to the change in its kinetic energy. This is applicable:

The rain drop of mass $1 \text{ g}$,starts with zero velocity from a height of $1 \text{ km}$. It hits the ground with a speed of $5 \text{ m/s}$. The work done by the unknown resistive force is . . . . . . $J$. (take $g = 10 \text{ m/s}^2$)

$A$ bullet of mass $10 \; g$ leaves a rifle at an initial velocity of $1000 \; m/s$ and strikes the earth at the same level with a velocity of $500 \; m/s$. The work done in joule $(J)$ in overcoming the resistance of air will be:

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