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The weight of a body on the surface of the earth is 63 N . When the body is moved to a height half of the radius of the earth, calculate the weight of the body.
Answers
Weight of the body, W = 63 N
Acceleration due to gravity at height h from the Earth’s surface is given by the relation:
g‘ = g / [1 + ( h / Re) ]2
Where,
g = Acceleration due to gravity on the Earth’s surface
Re = Radius of the Earth
For h = Re / 2
g‘ = g / [(1 + (Re / 2Re) ]2
= g / [1 + (1/2) ]2 = (4/9)g
Weight of a body of mass m at height h is given as:
W‘ = mg
= m × (4/9)g = (4/9)mg
= (4/9)W
= (4/9) × 63 = 28 N.
Answer:
Weight of the body, W = 63 N
Acceleration due to gravity at height h from the Earth’s surface is given by the relation:
g' = g / [1 + ( h / Re) ]2
Where,
g = Acceleration due to gravity on the Earth’s surface
Re = Radius of the Earth
For h = Re / 2
g' = g / [(1 + (Re / 2Re) ]2
= g / [1 + (1/2) ]2 = (4/9)g
Weight of a body of mass m at height h is given as:
W' = mg
= m × (4/9)g = (4/9)mg
= (4/9)W
= (4/9) × 63 = 28 N.