Question

Two balls of same mass are projected one vertically upwards and the other at angle 60⁰ with the vertical. The ratio of their potential energy at the highest point is

• A. 3 : 2
• B. 2 : 1
• C. 4 : 1
• D. 4 : 3

Answer 1

Answer: (C)

4 : 1

Answer 2

Potential energy at the highest point is given by $PE = \frac{1}{2}mu^{2}\sin^{2}\theta$

For first ball $\theta = 90{^\circ}$ ∴ $(PE)_{1} = \frac{1}{2}mu^{2}$

For second ball $\theta = (90^{o} - 60^{o}) = 30{^\circ}$ from the horizontal ∴ $(PE)_{2} = \frac{1}{2}mu^{2}\sin^{2}30{^\circ}$ $= \frac{1}{8}mu^{2}$

∴ $\frac{(PE)_{I}}{(PE)_{II}} = 4:1$