Match list-I with list-II:List-IList-II(A)Kinetic energy of plant(I) -GMm/a(B) Gravaitatioin potentiyal energy of sun -plant system(II) GMm/2 a(C)Total mecaniacal energy of palnt(III) Gm/r(D)Escap energyat the surface of plant for unit mass object(IV) -GMm/2 a(Where a= radius of planet orbit, r= radius of planet, M= mass of Sun, m= mass of planet) Choose the correct answer from the options given below:

(B) (A) - III, (B) - IV, (C) - I, (D) - II

(C) (A) - I, (B) - IV, (C) - II, (D) - III

(D) (A) - I, (B) - II, (C) - III, (D) - IV

JEE Mains · Physics · STD 11 - Gravitation

Match list-\(I\) with list-\(II\):
List-\(I\) List-\(II\)
\((A)\)Kinetic energy of plant \((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
\((B)\) Gravaitatioin potentiyal energy of sun -plant system \((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\((C)\)Total mecaniacal energy of palnt \((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
\((D)\)Escap energyat the surface of plant for unit mass object \((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
(Where \(\mathrm{a}=\) radius of planet orbit, \(\mathrm{r}=\) radius of planet, \(M=\) mass of Sun, \(m=\) mass of planet)
Choose the correct answer from the options given below:

Pick an option to check your answer.

Verified Solution

Correct Answer

(A) \((A) - II, (B) - I, (C) - IV, (D) - III\)

Detailed explanation

\(\mathrm{KE}=\frac{1}{2} \mathrm{mv}^2=\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\(\mathrm{PE}=-2 \mathrm{KE}\)
\(\mathrm{TE}=-\mathrm{KE}\)

Same subject

From JEE Mains

List-\(I\)	List-\(II\)
\((A)\)Kinetic energy of plant	\((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
\((B)\) Gravaitatioin potentiyal energy of sun -plant system	\((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\((C)\)Total mecaniacal energy of palnt	\((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
\((D)\)Escap energyat the surface of plant for unit mass object	\((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)