Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
**Assertion A:** The kinetic energy needed to project a body of mass $m$ from the earth's surface to infinity is $\dfrac12mgR$, where $R$ is the radius of the earth.
**Reason R:** The maximum potential energy of a body is zero when it is projected to infinity from the earth's surface.
In the light of the above statements, choose the correct answer from the options given below:
Answer: (A) A is false but R is true
The potential energy at the surface is $-\dfrac{GMm}{R} = -mgR$, and it rises to its maximum value, zero, at infinity. So R is true.
To reach infinity the body needs $K = mgR$ (escape speed $\sqrt{2gR}$), not $\tfrac12mgR$. A is false.
Solution by Sreeraj P, M.Sc Physics