## a heavenly body has a mass and radius half that of the earth. find the weight of a body on its surface if its mass is 100kg.

Question

a heavenly body has a mass and radius half that of the earth. find the weight of a body on its surface if its mass is 100kg.

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1 year 2021-09-05T05:33:35+00:00 1 Answers 10 views 0

Weight = 3891.6 N

Explanation: Given that a body has half of the mass and the radius of the earth, that is,

Mass M = 1/2 × 5.972 × 10^24 kg

Where 5.972 × 10^24 kg is the mass of the earth.

M = mass of the body

M = 2.986 × 10^24 kg

r = 1/2 × 6400 m

Where 6400 kilometre is the radius of the earth and r is the radius of the body.

r = 3200 km

To find the weight, let us first find the gravitational strength of the object by using the formula

g = GM/r^2

Where G = 6.67408 × 10-11 m3kg-1 s-2

g = (6.67408 × 10^-11 × 5.972 × 10^24 ) ÷ (3200 ×1000) ^2

g = 3.985 × 10^14/1.024 × 10^13

g = 38.9 m/s^2

Formula for weight = mg

Where m = 100kg

Weight = 100 × 38.9

Weight = 3891.6 N