KEAM 2015 Physics and Chemistry Paper

Gravitational potential energy of a body at a point is defined as the amount of work done in bringing the given body from infinity to that point against gravitational force
i.e. Gravitational potential energy = Gravitational potential × mass of the body
Given, R1=3R,R2=5R
In the first condition,
E1=−‌

GMm

R1

E1=−‌

GMm

3R

.....(i)
In the second condition,
E2=−‌

GMm

R2

E2=−‌

GMm

5R

.....(ii)
Change in energy required to lift it,
∆E=E2−E1
⇒‌‌∆E=−‌

GMm

5R

+‌

GMm

3R

⇒‌‌∆E=‌

2

15

‌

GMm

R

.....(iii)
On dividing Eq. (ii) by Eq. (i), we get
‌

∆E

E1

=‌

2

15

×‌

3

1

=‌

2

5

=0.4
‌

∆E

E

×100%=0.4×100=40%