$A$ satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
- Athe acceleration of $S$ is always directed towards the centre of the earth
- Bthe angular momentum of $S$ about the centre of the earth changes in direction,but its magnitude remains constant
- Cthe total mechanical energy of $S$ varies periodically with time
- Dthe linear momentum of $S$ remains constant in magnitude
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The solar constant on the surface of the earth is $S$. What will be its value on the surface of another planet which is about $5.3 \, AU$ away from the sun?
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View SolutionIn the following four periods:
$(i)$ Time of revolution of a satellite just above the earth's surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth's radius in a uniform field of $9.8 \; N/kg \; ({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth's real gravitational field $({T_{is}})$
$(i)$ Time of revolution of a satellite just above the earth's surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth's radius in a uniform field of $9.8 \; N/kg \; ({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth's real gravitational field $({T_{is}})$
Difficult
View SolutionMatch List-$I$ with List-$II$:
List-$I$ List-$II$ $(A)$ Kinetic energy of planet $(1)$ $-\frac{GMm}{a}$ $(B)$ Gravitational potential energy of Sun-planet system $(2)$ $\frac{GMm}{2a}$ $(C)$ Total mechanical energy of planet $(3)$ $\frac{GM}{r}$ $(D)$ Escape energy at the surface of planet for unit mass object $(4)$ $-\frac{GMm}{2a}$
(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:
| List-$I$ | List-$II$ |
| $(A)$ Kinetic energy of planet | $(1)$ $-\frac{GMm}{a}$ |
| $(B)$ Gravitational potential energy of Sun-planet system | $(2)$ $\frac{GMm}{2a}$ |
| $(C)$ Total mechanical energy of planet | $(3)$ $\frac{GM}{r}$ |
| $(D)$ Escape energy at the surface of planet for unit mass object | $(4)$ $-\frac{GMm}{2a}$ |
(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:
DifficultJEE MAIN 2024
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