Question

The kinetic energy needed to project a body of mass $m$ from the earth's surface to infinity is

• A. $\frac{1}{4}mgR$
• B. $\frac{1}{2}mgR$
• C. $mgR$
• D. $2mgR$

Answer 1

The correct option is C $mgR$

The total energy of a particle is sum of potential and kinetic energies i.e.$T.E.=P.E.+K.E.$
For a stationary mass m on earth$,P.E.=-mgr$ and $K.E.=0$.
Thus,
$T.E.=-mgr$ where $g$ is acceleration due to gravity.
At infinity$,P.E.$ is zero for a body and let that the body has to jst reach inifinity. So $K.E.$ is also zero.
Therefore, final required total energy i.e. $R.T.E.=0+0=0$.
Now, the required energy is to be given in form of kinetic energy and let it be $K$.
So$,R.T.E.=T.E.+extrakineticenergy=-mgr+K$.
Thus the required kinetic energy is $K=mgr$.