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7.Gravitation
hard
Match list-$I$ with list-$II$:
| List-$i$ | List-$2$ |
| $(A)$Kinetic energy of plant | $(1)$ $-\frac{\mathrm{GMm}}{\mathrm{a}}$ |
| $(B)$ Gravaitatioin potentiyal energy of sun -plant system | $(2)$ $\frac{\mathrm{GMm}}{2 \mathrm{a}}$ |
| $(C)$Total mecaniacal energy of palnt | $(3)$ $\frac{\mathrm{Gm}}{\mathrm{r}}$ |
| $(D)$Escap energyat the surface of plant for unit mass object | $(4)$ $-\frac{\mathrm{GMm}}{2 \mathrm{a}}$ |
(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:
A
$(A) - II, (B) - I, (C) - IV, (D) - III$
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 MAIN-2024)
Solution
$\mathrm{KE}=\frac{1}{2} \mathrm{mv}^2=\frac{\mathrm{GMm}}{2 \mathrm{a}}$
$\mathrm{PE}=-2 \mathrm{KE}$
$\mathrm{TE}=-\mathrm{KE}$
Standard 11
Physics
