Question

If a body is to be projected vertically upwards
from earth's surface to reach a height of 10 R
where R is the radius of earth. The velocity
required to do so is

Answer 1

$\huge\underline\mathfrak\red{Answer}$

BASIC CONCEPT USED

• WHEN NO EXTERNAL FORCE IS APPLIED ON A SYSTEM THAN THE TOTAL ENERGY AT ANY INSTANT REMAINS SAME UNTIL AND UNLESS YOU APPLIED A EXTERNAL FORCE THIS IS KNOWN AS LAW OF CONVERSATION OF ENERGY.

$let \: the \: velocity \: v \: is \: require \:to \\ reach \: at \: 10r \\ \\ than \: \: kinetic \: energy \: of \: the \: body \\ \\ \frac{1}{2} m {v}^{2} ........(1) \\ \\ the\: potential \: at \: a \: height \: of\: 10r \: will \:be \ \\ \\ \ mg(10r)....(2) \\ \\ acc \: to \: law \: of \: conversation \: of \: energy \\ \\ \frac{1}{2} m {v}^{2} = mg(10r) \\ \\ {v}^{2} = 20gr \\ \\ v = \sqrt{20gr} \\ \\ where \: m \: is \: the \: mass \: of \: the \: body \\ r \: is \: the \: radius \: of \: the \: earth \\ v \: is \: velocity \: required$

PRECAUTIONS

• WHEN YOU DEALING WITH POTENTIAL ENERGY THAN MAKE SURE THAT THE REFERENCE POINT IS MENTION. OR IF NOT MENTION THAN YOU WILL CHOSE ACC TO YOUR CONVINENCE I HAD CHOSE CENTER OF THE EARTH AS THE REFERENCE POINT