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Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g’, then [2005]
  • a)
    g’ = g/9
  • b)
    g’ = 27g
  • c)
    g’=9g
  • d)
    g’=3g
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Imagine a new planet having the same density as that of earth but it i...
We know that
∴  g ' = 3g
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Imagine a new planet having the same density as that of earth but it i...
Given that the new planet has the same density as Earth but is 3 times bigger in size, we can assume that the mass of the new planet is also 3 times greater than Earth's mass. Let's denote the mass of Earth as M and the mass of the new planet as 3M.

The acceleration due to gravity, g, is given by the formula:

g = (G * M) / r^2

where G is the gravitational constant and r is the radius of the planet.

Since the new planet is 3 times bigger in size, we can assume that its radius is also 3 times greater than Earth's radius. Let's denote Earth's radius as R and the new planet's radius as 3R.

Now, let's calculate the acceleration due to gravity on the surface of the new planet:

g_new = (G * (3M)) / (3R)^2
= (G * (3M)) / 9R^2
= (1/3) * ((G * M) / R^2)
= (1/3) * g

Therefore, the acceleration due to gravity on the surface of the new planet is (1/3) times the acceleration due to gravity on Earth's surface.
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Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g’, then [2005]a)g’ = g/9b)g’ = 27gc)g’=9gd)g’=3gCorrect answer is option 'D'. Can you explain this answer?
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