A stone is projected vertically upwards with velocity ' $\mathrm{V}$. Another stone of same mass is…
A stone is projected vertically upwards with velocity ' $\mathrm{V}$.
Another stone of same mass is projected at an angle of $60^{\circ}$ with the vertical with the same speed (V). The ratio of their potential energies at the highest points of their journey, is
1:1
4:1
3:2
2:1
Solution
Maximum height, $\mathrm{h}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}$
For the first stone $\theta=90^{\circ}, \sin 90^{\circ}=1$
$\therefore \mathrm{h}_1=\frac{\mathrm{u}^2}{2 \mathrm{~g}}=\frac{\mathrm{V}^2}{2 \mathrm{~g}}$
For the second stone, $\mathrm{h}_2=\frac{\mathrm{v}^2 \sin ^2 30^{\circ}}{2 \mathrm{~g}}=\frac{\mathrm{V}^2}{8 \mathrm{~g}}$ The masses are same. Hence ratio of potential energies
$\frac{\mathrm{U}_1}{\mathrm{U}_2}=\frac{\mathrm{h}_1}{\mathrm{~h}_2}=4$