$A$ body situated on the surface of the earth becomes weightless at the equator when the rotational kinetic energy of the earth reaches a critical value '$K$'. The value of '$K$' is given by [$g$ = gravitational acceleration on earth's surface,$M$ = mass of the earth,and $R$ = radius of the earth].
- A$\frac{1}{2} MgR$
- B$\frac{1}{3} MgR$
- C$\frac{1}{4} MgR$
- D$\frac{1}{5} MgR$
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Similar Questions
For a satellite to orbit around the earth,which of the following must be true?
Difficult
View SolutionMatch the column $-I$ with column $-II$ for a satellite in circular orbit:
Column $-I$ Column $-II$ $(A)$ Kinetic energy $(p)$ $-\frac{GM_Em}{2r}$ $(B)$ Potential energy $(q)$ $\sqrt{\frac{GM_E}{r}}$ $(C)$ Total energy $(r)$ $-\frac{GM_Em}{r}$ $(D)$ Orbital velocity $(s)$ $\frac{GM_Em}{2r}$
(where $M_E$ is the mass of the earth,$m$ is the mass of the satellite,and $r$ is the radius of the orbit)
| Column $-I$ | Column $-II$ |
| $(A)$ Kinetic energy | $(p)$ $-\frac{GM_Em}{2r}$ |
| $(B)$ Potential energy | $(q)$ $\sqrt{\frac{GM_E}{r}}$ |
| $(C)$ Total energy | $(r)$ $-\frac{GM_Em}{r}$ |
| $(D)$ Orbital velocity | $(s)$ $\frac{GM_Em}{2r}$ |
(where $M_E$ is the mass of the earth,$m$ is the mass of the satellite,and $r$ is the radius of the orbit)
Medium
View SolutionFill in the blanks:
$(a)$ The value of gravitational intensity at the center of the Earth is ..... .
$(b)$ The potential energy of a satellite is $-8 \times 10^9 \, J$,then its binding energy is ............ .
$(c)$ Kepler's second law regarding the constancy of the areal velocity of a planet is a consequence of the law of conservation of .......... .
$(a)$ The value of gravitational intensity at the center of the Earth is ..... .
$(b)$ The potential energy of a satellite is $-8 \times 10^9 \, J$,then its binding energy is ............ .
$(c)$ Kepler's second law regarding the constancy of the areal velocity of a planet is a consequence of the law of conservation of .......... .
Medium
View SolutionThe mass density of a spherical body is given by $\rho(r) = \frac{k}{r}$ for $r \leq R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the centre. The correct graph that describes qualitatively the acceleration,$a$,of a test particle as a function of $r$ is
DifficultJEE MAIN 2017
View Solution$A$ particle is dropped on Earth from a height $R$ (radius of Earth) and it bounces back to a height $R/2$. The coefficient of restitution for the collision is (ignore air resistance and rotation of Earth).
Difficult
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