Question

Two identical pendulums are tied from the same rigid support. One is tied horizontally as shown in the figure. The other is released when they are making the same angle $\theta$ with the vertical. The ratio of tensions $\frac{T_1}{T_2}$ is given as

• A. ${\tan }^2\theta$
• B. ${\cot }^2\theta$
• C. $1$
• D. ${\sec }^2\theta$

Answer 1

Answer: (D)

${\sec }^2\theta$

$T_1\cos \theta =mg$
$⟹T_1=\frac{mg}{\cos \theta }$
$⟹T_2=mg\cos \theta$
$\therefore \frac{T_1}{T_2}=\frac{1}{{\cos }^2\theta }={\sec }^2\theta$