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JEE Mains · Physics · STD 11 - 7. 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:

  1. A \((A) - II, (B) - I, (C) - IV, (D) - III\)
  2. B \((A) - III, (B) - IV, (C) - I, (D) - II\)
  3. C \((A) - I, (B) - IV, (C) - II, (D) - III\)
  4. D \((A) - I, (B) - II, (C) - III, (D) - IV\)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

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