Question

A ball attached to one end of a string swings in a vertical plane such that its acceleration at point A (extreme position) is equal to its acceleration at point B (mean position). The angle $\theta$ is

• A. ${\cos }^{-1}\left(\frac{2}{5}\right)$
• B. ${\cos }^{-1}\left(\frac{4}{5}\right)$
• C. ${\cos }^{-1}\left(\frac{3}{5}\right)$
• D. None of these

Answer 1

Answer: (C)

${\cos }^{-1}\left(\frac{3}{5}\right)$

Let acceleration at both points be 'a'.

At point A, $mg\sin \theta =ma$

At point B, $\frac{m{v}^2}{r}=ma$

By energy conservation, $\frac{m{v}^2}{2}=mgr\times (1-\cos \theta )$

Solving, to get $\cos \theta =-1or\frac{3}{5}$

=> θ = ${\cos }^{-1}\frac{3}{5}$