Answer :
(a) The acceleration due to gravity on the given planet is 11.2 m/s².
(b) A person with a mass of 59.1 kg would weigh 662.7 N on this planet.
(a) The acceleration due to gravity on the given planet can be calculated using the formula:
g = (G × M) / r²
Where G is the universal gravitational constant, M is the mass of the planet, and r is its radius.
Given,
M = 5.37×10²³ kg
r = 2.77×10⁶ m
G = 6.67×10⁻¹¹ N m² / kg²
Substituting the values in the above formula, we get:
g = (6.67×10⁻¹¹ × 5.37×10²³) / (2.77×10⁶)²
g = 11.2 m/s²
Therefore, the acceleration due to gravity on this planet is 11.2 m/s².
(b) To calculate the weight of a person on this planet, we use the formula:
W = mg
Where W is the weight, m is the mass of the person, and g is the acceleration due to gravity on the planet.
Given,
m = 59.1 kg
g = 11.2 m/s²
Substituting the values in the above formula, we get:
W = 59.1 × 11.2
W = 662.7 N
Therefore, a person with a mass of 59.1 kg would weigh 662.7 N on this planet.
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