If kinetic energy of a body is given as $k = C x$ where $C$ is constant and $x$ is distance from origin then, dimensional formula for $C$ is

[M L T^{- 1}]

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[M L T]

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[M^{\circ} L^{2} T^{- 1}]

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[M L T^{- 2}]

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Solution

The correct option is D $[M L T^{- 2}]$
$K = c x \Rightarrow \frac{1}{2} m v^{2} = c x$
$\Rightarrow M L^{2} T^{- 2} = [C] L^{1} \Rightarrow [C] = M L^{1} T^{- 2}$

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