Question

What kind of relation exists between the kinetic energy (E) and the orbital radius (r) of the satellites revolving around the earth?.
(A) E ∝ r
(B) E ∝ 1/r
(C) E ∝ r²
(D) E ∝ 1/r²

Answer 1

Answer:

(B) E ∝ $\frac{1}{r}$

Explanation:

for the circular orbit ,gravitational force should be equal to  centripetal force to  move the axis in a uniform circular motion , therefore:

                              $F_{g}=F_{c}$

                              $\frac{mv^{2}}{r}=\frac{GMm}{r^{2}}$

where r= orbital radius

                               ∴$v^{2}=\frac{GM}{r}$

now substitute the value of $v^{2}=\frac{GM}{r}$ in the formula of kinetic energy which is equals to

                           $K.E=\frac{1}{2}mv^{2}$

                           $K.E=\frac{1}{2}m\frac{GM}{r}$

which indicate that kinetic energy is inversely proportional to the orbital radius.

Answer 2

Answer:

option:- B

is correct ,i.e. E 1/r