Q. A heavy particle hanging from a fixed point by a light inextensible string of length ' $\ell$ ' is projected horizontally with speed $\sqrt{g \ell}$, the speed of the particle is $\sqrt{\frac{g \ell}{a}}$ and the inclination of the string to the vertical is $\cos ^{-1} \frac{2}{b}$ at the instant of the motion when the tension in the string is equal to the weight of the particle. Determine $\frac{a}{b}$.
Laws of Motion
Solution: