How does the acceleration due to gravity $(g)$ at a location on Earth change with latitude?

  • A
    It decreases as we move from the equator to the poles.
  • B
    It increases as we move from the equator to the poles.
  • C
    It remains constant at all latitudes.
  • D
    It is maximum at the equator and minimum at the poles.

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The ratio of the radii of a planet and the earth is $1: 2$, and the ratio of their mean densities is $4: 1$. If the acceleration due to gravity on the surface of the earth is $9.8 \,ms^{-2}$, then the acceleration due to gravity on the surface of the planet is: (in $\,ms^{-2}$)

The radius of the Earth is approximately $6000 \, km$. The weight of a body at a height of $6000 \, km$ from the Earth's surface becomes:

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other possesses simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?

Give the value of acceleration due to gravity at height $12\, km$ from the surface of earth. (in $, m/s^2$)

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