A stone is projected vertically upwards with speed ' v '. Another… - Vidyadip

MCQ

A stone is projected vertically upwards with speed ' $v$ '. 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 $\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right]$

✓
$4: 1$
B
$3: 2$
C
$2: 1$
D
$1: 1$

✓

Answer

Correct option: A.

$4: 1$

(a) : At highest point whole kinetic energy will convert into potential energy.
$
\begin{aligned}
\therefore \quad & PE _A= KE =\frac{1}{2} m v^2 \\
& H_B=\frac{v^2 \sin ^2 30^{\circ}}{2 g} ; H_B=\frac{v^2 \times 1}{8 g}
\end{aligned}
$
So, $P E_B=\frac{m g v^2 \times 1}{8 g}=\frac{1}{8} m v^2$
So, $\frac{P E_A}{P E_B}=\frac{\frac{1}{2} m v^2}{\frac{1}{8} m v^2}=4: 1$

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