What is the acceleration due to gravity on a planet that has a mass of 1.024 x 1026 kg and a radius of 2.5 x 107 m?

Use the law of universal gravitation, which says the force due to gravity between two bodies of masses m₁ and m₂ separated by a distance r is

F = G m₁ m₂ / r²

(where G = 6.67 x 10⁻¹¹ N m²/kg²)

as well as Newton's second law, which says a force that acts on a body of mass m is proportional to its acceleration a such that

F = m a

So we have

G m₁ m₂ / r² = m a

m is the same mass as one of the masses used on the left side:

G m / r² = a

a = (6.67 x 10⁻¹¹ N m²/kg²) (1.024 x 10²⁶ kg) / (2.5 x 10⁷ m)²

a ≈ 10.93 m/s²

the correct choice is a .

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