Question

Two balls of same mass are projected with the same speed one vertically upwards and the other at angle ${60}^{\circ }$ 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

The correct option is C 4 : 1

Potential energy at the highest point is given by $PE=\frac{1}{2}m{u}^{2}si{n}^2\theta$
For first ball $\theta ={90}^{\circ }\therefore (PE{)}_1=\frac{1}{2}m{u}^2$
For second ball $\theta =({90}^{\circ }-{60}^{\circ }={30}^{\circ }$ from the horizontal $\therefore (PE{)}_1=\frac{1}{2}m{u}^{2}si{n}^2{30}^{\circ }=\frac{1}{8}m{u}^2$
$\therefore \frac{(PE{)}_I}{(PE{)}_{II}}=4:1$