Question
Assuming potential energy 'U' at ground level to be zero.
All objects are made up of same material.
UP = Potential energy of solid sphere
UQ = Potential energy of solid cube
UR = Potential energy of solid cone
US = Potential energy of solid cylinder
Options
Solution
Sol.
$U_{P} = mgR = \frac{4\pi}{3}\left( \frac{D}{2} \right)^{3}\rho g\frac{D}{2} = \frac{\pi}{12}\rho.D^{4}.g$
$U_{Q} = mg.\frac{D}{2} = D^{3}.\rho.g.\frac{D}{2}$
= $\frac{1}{2}\rho.D^{4}.g$
$U_{R} = mg.\frac{D}{4} = \frac{1}{3}\pi\left( \frac{D}{2} \right)^{2}$× $D\rho \times g.\frac{D}{4} = \frac{\pi}{48}\rho.D^{4}.g$
$U_{S} = m_{4} = \pi({D/}2)^{2}.DPg\frac{D}{2} = \frac{\pi}{8}\rho D^{4}.g$
(A) US > UP
(B) $\frac{1}{2} = 0.5$, $\frac{\pi}{8} = \frac{3.5v}{8}$ = 0.4
∴ UQ > US
(C) UP < UQ
(D) US > UR
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