Question

A body is thrown vertically up with certain initial velocity, the potential and kinetic energies of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of potential and kinetic energies of the body when it crosses the same point, is :

• A. $1:1$
• B. $1:4$
• C. $1:7$
• D. $1:8$

Answer 1

The correct option is C $1:7$

Let a point where, $\frac{1}{2}m{v}^2=mgh$

Total $M.E=2mgh$

Now, when $v$ is twice

Total $M.E=8mgh$

Now when the ball passes through that point

$K.E=8mgh-mgh$ $=7mgh$

$P.E=mgh$

$P.E:K.E=1:7$