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Sagot :
ANSWERS
(a) 5.04 m/s²
(b) 294.34 N
EXPLANATION
Given:
• The mass of the planet, M = 6.14 x 10²³ kg
,• The radius of the planet, R = 2.85 x 10⁶ m
,• The mass of a person standing on this planet, m = 58.4 kg
(a) The acceleration due to gravity in a planet of mass M and radius R is,
[tex]g=\frac{G\cdot M}{R^2}[/tex]Where G is the gravitational constant with a value of 6.67 x 10⁻¹¹ Nm²/kg².
Replacing the known values and solving we get the acceleration due to gravity of this planet,
[tex]g=\frac{6.67\cdot10^{-11}Nm^2/kg^2\cdot6.14\cdot10^{23}kg}{(2.85\cdot10^6)^2m^2}\approx5.04m/s^2[/tex]Hence, the acceleration due to gravity is 5.04 m/s², rounded to two decimal places.
(b) The weight of an object of mass m is the product of its mass and the acceleration due to gravity,
[tex]weight=m\cdot g=58.4kg\cdot5.04m/s^2\approx294.34N[/tex]Hence, a 58.4-kg person would weigh 294.34 N on this planet, rounded to two decimal places.
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