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Q. In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is

MHT CETMHT CET 2016

Solution:

Velocity at the lowest point of the vertical circular motion $v_{h}=\sqrt{5 g 1}$
Velocity at the highest point of the vertical circular motion $v _{1}=\sqrt{ gl }$
where 1 is the radius of the vertical circular motion.
Thus ratio of kinetic energy at the highest to the lowest point $\frac{ K \cdot E _{ h }}{ K \cdot E _{1}}=\frac{ m v _{ h }^{2} / 2}{ mv _{1}^{2} / 2}=\frac{ v _{ h }^{2}}{ v _{1}^{2}}$
$\Rightarrow \frac{ K \cdot E _{ h }}{ K \cdot E _{1}}=\frac{ gl }{5 gl }=0.2$