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The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be
  • a)
    ½ R
  • b)
    2 R [2004]
  • c)
    4 R
  • d)
    1/4 R
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The density of a newly discovered planet is twice that of earth. The a...
At the surface of planet, 
At the surface of the earth 
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The density of a newly discovered planet is twice that of earth. The a...
The acceleration due to gravity at the surface of a planet can be calculated using the formula:

g = G * M / R^2

where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Since the acceleration due to gravity at the surface of the newly discovered planet is equal to that at the surface of the earth, we can write:

G * M_planet / R_planet^2 = G * M_earth / R_earth^2

where M_earth and R_earth are the mass and radius of the earth, respectively.

We are also given that the density of the newly discovered planet is twice that of earth. The density of a planet can be calculated using the formula:

density = M / (4/3 * pi * R^3)

where M is the mass of the planet and R is the radius of the planet.

Since the density of the newly discovered planet is twice that of earth, we can write:

M_planet / (4/3 * pi * R_planet^3) = 2 * M_earth / (4/3 * pi * R_earth^3)

Simplifying this equation, we get:

M_planet / R_planet^3 = 2 * M_earth / R_earth^3

Multiplying both sides by R_planet^2, we get:

M_planet / R_planet = 2 * M_earth / R_earth

Substituting this into the earlier equation, we get:

G * (2 * M_earth / R_earth) / R_planet^2 = G * M_earth / R_earth^2

Simplifying this equation, we get:

R_planet = sqrt(2) * R_earth

Therefore, the radius of the newly discovered planet is sqrt(2) times the radius of the earth.
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The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would bea)½ Rb)2 R [2004]c)4 Rd)1/4 RCorrect answer is option 'A'. Can you explain this answer?
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