Question

State and prove law of conservation of energy in case of freely falling body?

Answer 1

Law of conservation of energy states that$:-$

Energy can neither be created nor be destroyed$.$

Energy transforms from one form to another form and$,$ potential energy$+$ kinetic energy$=$ constant

Proof$:-$

At point $A$

$K.E=0m/s$

$P.E=mgh$

$P.E=mgh$

At point $B,$

$K.E.,$

$2gh=V^2-O^2$

$V^2=2gx$

$K.E=\frac{1}{2}m{V}^2$

$K.E=\frac{1}{2}m.2gx$

$K.E=mgx$-----------------------------$\left(1\right)$

$P.E=mgh$

$P.E=m.g.\left(h-x\right)$

$P.E=mgh-mgx$---------------------$\left(2\right)$

from$\left(1\right)$ and $\left(2\right)$

$K.E+P.E$ constant

$mgx+mgh-mgx=mgh$

$mgh=mgh$

At point $C,$

$P.E=0$

$2gh=v^2-u^2$ $($ initial velocity $=0$ m/s$)$

$2gh=v^2$

$K.E=\frac{1}{2}.m.v$

$K.E=\frac{1}{2}.m.2gh$

$K.E=mgh$

Thus$,$ in all the points the energy is same$.$