Question

Two simple pendulum of lengths $1$m and $2$m have identical bobs and oscillating with same amplitudes. Their energies are in the ratio

• A. 1: 2
• B. 2 : 1
• C. 4 : 1
• D. 1 : 4

Answer 1

The correct option is B 2 : 1

$T_1=2\pi \sqrt{\frac{1}{g}};T_2=2\pi \sqrt{\frac{2}{g}}$
$w_1=\sqrt{g};w_2=\sqrt{\frac{g}{2}}$
$E_1=\frac{1}{2}m{w}_1^2{A}^2$
$E_2=\frac{1}{2}m{w}_2^2{A}^2$
$\frac{E_1}{E_2}=\frac{2}{1}$