Question

In vertical circular motion, the ratio of kinetic energy to potential energy at the horizontal position is ____________.

• A. $5:2$
• B. $2:1$
• C. $3:2$
• D. $2:3$

Answer 1

Answer: (C)

$3:2$

We assume that the object in motion just manages to complete the vertical circle. In that case,

$v_{top}=\sqrt{gR}$
Total energy at the topmost point $=\frac{1}{2}mgR+2mgR=\frac{5}{2}mgR$

At the horizontal position $PE=mgR$

Total energy $=\frac{5}{2}mgR$

$\therefore KE=(\frac{5}{2}-1)=\frac{3}{2}mgR$

$\therefore \frac{KE}{PE}=\frac{3}{2}$