Question

Assuming potential energy ${}^{\prime }{U}^{\prime }$ at ground level to be zero.

All objects are made up of same material.
$U_p=$ Potential energy of solid sphere
$U_Q=$ Potential energy of solid cube
$U_R=$ Potential energy of solid cone
$U_S=$ Potential energy of solid cylinder

• A. $U_S>U_P$
• B. $U_Q>U_S$
• C. $U_P>U_Q$
• D. $U_P>U_S$

Answer 1

Answer: (A), (B)

The correct options are
A $U_S>U_P$
B $U_Q>U_S$

let density of material be $\rho$
mass of the object is $m=\rho V$
$U$ potential energy $=\rho Vgh$
Here $h$ is height of center of mass of the object from the ground level.

For Solid sphere
$V=\frac{\pi D^3}{6},h=\frac{D}{2}$
$U_P=\frac{\rho g\pi D^4}{12}$
For Cube
$V=D^3,h=\frac{D}{2}$
$U_Q=\frac{\rho g{D}^4}{2}$
For cone
$V=\frac{\pi D^3}{12},h=\frac{D}{3}$
$U_R=\frac{\rho g\pi D^4}{36}$
For Solid cylinder
$V=\frac{\pi D^3}{4},h=\frac{D}{2}$
$U_S=\frac{\rho g\pi D^4}{8}$
on solving $U_Q>U_S>U_P>U_R$
Hence, option (a) and (b) are correct.