Question

When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point $A$ are in the ratio $2:3$. If the same body is projected with double the previous velocity, then at the same point $A$ the ratio of its potential energy to kinetic energy is

• A. $9:1$
• B. $2:9$
• C. $1:9$
• D. $9:2$
• E. $3:2$

Answer 1

The correct option is C $1:9$

Let in the first case, the total energy at the throwing point be $5E$.
$KE$ at a particular height $=3E$, potential energy at the height $=2E$
As velocity of thrown is doubled, kinetic energy becomes $4$ times.
$\therefore$ Total $KE$ at the throwing point $20E$
$PE$ at the same height $=2E$ (will remain same as the previous value) and $KE$ at the same height $=18E$
$\frac{PE}{KE}=\frac{2E}{18E}=\frac{1}{9}=1:9$.