KEAM 2014 Physics and Chemistry Paper

We know that,
U=−‌

GMem

R

.....(i)
and gravitational kinetic energy
K=‌

1

2

⋅‌

GMem

R

....(ii)
∴ Total energy of a body is
E=U+K
=−‌

GMem

R

+‌

GMem

2R

But, acceleration due to gravity (g) in terms of gravitational constant (G) is
g=‌

GMe

R2

.....(iii)
∴‌‌−‌

GMe

R2

×R2×‌

m

2R

[From Eq. (iii)]
=g×R2×‌

m

2R

(Cancelation of negative sign, because energy can never be negative)
=‌

gmR

2

=‌

mgR

2