The angular velocity and amplitude of a simple pendulum are 'w' and A respectively. At a displacement 'x'. if its KE is 'T' and Pe is 'U' then the ratio of 'T' to 'U' is

\frac{x^{2} w^{2}}{A^{2} - w^{2} x^{2}}

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\frac{x^{2}}{A^{2} - x^{2}}

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\frac{A^{2} - w^{2} x^{2}}{x^{2} w^{2}}

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\frac{A^{2} - x^{2}}{x^{2}}

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Solution

The correct option is D $\frac{A^{2} - x^{2}}{x^{2}}$
For a simple pendulum, expression for KE and PE is :
$K E = T = \frac{1}{2} m w^{2} (A^{2} - x^{2})$ [x: displacement]
$P E = u = \frac{1}{2} m w^{2} x^{2}$
on taking Ratio,
$\frac{T}{u} = \frac{A^{2} - x^{2}}{x^{2}}$

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