Question

The angular velocity and the amplitude of a simple pendulum is $\omega$ 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

• A. $X^{2}\omega^{2}/(a^{2} - X^{2}\omega^{2})$
• B. $X^{2}/(a^{2} - X^{2})$
• C. $(a^{2} - X^{2}\omega^{2})/X^{2}\omega^{2}$
• D. $(a^{2} - X^{2})/X^{2}$

Answer 1

Answer: (D)

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

Answer 2

Kinetic energy $T = \frac{1}{2}m\omega^{2}(a^{2} - x^{2})$

and potential energy,

$V = \frac{1}{2}m\omega^{2}x^{2}$ $\therefore\frac{T}{V} = \frac{a^{2} - x^{2}}{x^{2}}$