Question 328: Work, Energy and Power & Circular Motion

Question

A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest position are equal. The angle $	heta$ of thread deflection in the extreme position will be

Accepted Answer

$$ \begin{array}{r} g \sin 	heta=\frac{v^2}{R}=\frac{2 g h}{R}=\frac{2 g R(1-\cos 	heta)}{R} \ \{\because h=R(1-\cos 	heta)\} \end{array} $$
$$ \begin{aligned} & 	ext { or } \sin 	heta=2(1-\cos 	heta) \ & 2 \sin \frac{	heta}{2} \cos \frac{	heta}{2}=2\left(2 \sin ^2 \frac{	heta}{2}ight) \ & 	herefore \quad 	an \frac{	heta}{2}=\frac{1}{2} \ & \qquad \quad \frac{	heta}{2}=	an ^{-1}\left(\frac{1}{2}ight) \ & 	ext { or } \quad 	heta=2 	an ^{-1}\left(\frac{1}{2}ight) \end{aligned} $$

Answer

$	an ^{-1}(2)$

Answer

$	an ^{-1}(\sqrt{2})$

Answer

$	an ^{-1}\left(\frac{1}{2}ight)$

Answer

$2 	an ^{-1}\left(\frac{1}{2}ight)$

Work, Energy and Power & Circular Motion

A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest position are equal. The angle \theta of thread deflection in the extreme position will be

Choose the correct answer: