Question

A simple pendulum of length l is set in motion such that the bob, of mass m, moves along a horizontal circular path, and the string makes a constant angle $\theta$ with the vertical. The time period rotation of the bob is t and the tension in the thread is T.

• A. $t=2\pi \sqrt{l/g}$
• B. $t=2\pi \sqrt{l\cos \theta /g}$
• C. $T=\frac{4{\pi }^{2}ml}{t^2}$
• D. $Thebobisinequilibrium$

Answer 1

Answer: (B), (C)

The correct options are
B $t=2\pi \sqrt{l\cos \theta /g}$
C $T=\frac{4{\pi }^{2}ml}{t^2}$

Balancing the forces in Horizontal and vertical direction:

$Tsin\theta =m{\omega }^{2}l\times sin\theta orT=m{\omega }^{2}l$

$Tcos\theta =mgorm{\omega }^{2}lcos\theta =mgor{\omega }^2=\frac{g}{lcos\theta }t=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{lcos\theta }{g}}T=m\left[\frac{4{\pi }^2}{t^2}\right]l$