The angular velocity and the amplitude of a simple pendulum is $ω$ and a respectively. At a displacement X from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is

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$X^{2} ω^{2} / (a^{2} - X^{2} ω^{2})$

$X^{2} / (a^{2} - X^{2})$

$(a^{2} - X^{2} ω^{2}) / X^{2} ω^{2}$

$(a^{2} - X^{2}) / X^{2}$

answer is D.

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Detailed Solution

Kinetic energy $T = \frac{1}{2} {mω}^{2} (a^{2} - x^{2})$
and potential energy, $V = \frac{1}{2} {mω}^{2} x^{2}$

$∴ \frac{T}{V} = \frac{a^{2} - x^{2}}{x^{2}}$

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