Question

A pendulum is vibrating with an amplitude of π/2 radian. Value of αfor which resultant acceleration of the bob directs along the horizontal is

• A. sin^-1/$\sqrt{3}$
• B. cos^-11/$\sqrt{3}$
• C. cos^-1$\sqrt{3}$/2
• D. sin^-1$\sqrt{3}$/2

Answer 1

Answer: (B)

cos^-11/$\sqrt{3}$

Answer 2

Tangential acceleration, a_t = g sin α and radial

acceleration,

a_r = $\frac{v^{2}}{l} = \frac{2gl\cos\alpha}{l}$ = 2 g cos α

Also tan α = $\frac{a_{r}}{a_{t}}$

= $\frac{2g\cos\alpha}{g\sin\alpha} = \frac{2}{\tan\alpha}$

or tan²α = 2 i.e., sec² α = 3

or $\frac{1}{\cos^{2}\alpha} = 3$ or cos α = $\frac{1}{\sqrt{3}}$

or α = cos^-1$\frac{1}{\sqrt{3}}$