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Select the correct choice(s) :
The gravitational field insideaspherical cavity,with inaspherical planet must be non zero and uniform.
When a body is projected horizontally at an appreciable large height above the earth, with a velocity less than for a circular orbit, it will fall to the earth along a parabolic path.
Abody of zero total mechanical energy placed in a gravitational field will escape the field
Earth’s satellite must be in equatorial plane .
Solution
Gravitational field is conservative field, total mechanical energy is conserved. If a body is in gravitational field with $U+K=0 \rightarrow K=-U \rightarrow(1)$ i.e. Kinetic energy is non zero.So, it will move away from the field till its kinetic energy is also zero.
If $K=0 \rightarrow U=0$ from $(1).$ But, $U=0$ is at $\infty$ and thus the body escapes the field.
Similar Questions
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)
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