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Q.

Let a satellite of mass m is revolving in a circular orbit of radius r around a planet of mass M such that the system is bound. If E, U, K and B denote total energy potential energy, kinetic energy and binding energy respectively then match the following columns and select the correct option from the codes given below.
Column-I Column-II
i. E p. $\frac{GMm}{2 r}$
ii. U q. $\frac{GMm}{2 r}$
iii. K r. $- \frac{GMm}{r}$
iv. B s. $- \frac{GMm}{2 r}$
Codes

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a

i-q, ii-r, iii-s, iv-p

b

i-r, ii-s, iii-p, iv- q

c

i-s, ii-r, iii-q, iv-p

d

i-p, ii-q, iii-r, iv-s

answer is A.

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Detailed Solution

K = $\frac{1}{2} {mv}_{0}^{2} = \frac{1}{2} m {(\sqrt{\frac{GM}{r}})}^{2} = \frac{GMm}{2 r}$

U = $- \frac{GMm}{r}$

E = U + K = $- \frac{GMm}{r} + \frac{GMm}{2 r} = - \frac{GMm}{2 r}$

B = |E| = $\frac{GMm}{2 r}$

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Let a satellite of mass m is revolving in a circular orbit of radius r around a planet of mass M such that the system is bound. If E, U, K and B denote total energy potential energy, kinetic energy and binding energy respectively then match the following columns and select the correct option from the codes given below. Column-I Column-IIi.Ep.GMm2rii.Uq.GMm2riii. Kr.-GMmriv.Bs.-GMm2rCodes