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Question
A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
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Solution
Given:
- Force/weight of the body on earth = 5.6 kg wt
- Mass of the planet = 7 × Mass of Earth
- Radius of the planet = 2 times Radius of the Earth
To find: Weight of the body on the surface of the planet
Calculation:
Let the mass of Earth be 'm' kg.
Let the distance between the two bodies be 'r' m.
F = G`("m" " m"_2)/"r"^2` ...(i)
Force of Gravitation between the two bodies when mass of Earth is 7 times and the distance is doubled.
F' = G`(7 "m m"_2)/(2"r")^2`
F' = G`(7 "m m"_2)/(4"r"^2)` ...(ii)
Now, dividing Equation (i) from Equation (ii), we get:
`=> ("F'")/"F" = (cancel"G"(7 "m m"_2)/(4"r"^2))/(cancel"G"("m m"_2)/"r"^2`
`=> "F'"/"F" = (7 "m m"_2)/(4"r"^2) xx "r"^2/"m m"_2`
`=> "F'"/"F" = (7 cancel("m m"_2))/(4cancel("r"^2)) xx cancel("r"^2)/cancel("m m"_2)`
`=> "F'"/"F" = 7/4`
Now, by substituting the value of F in the Equation, we get:
`=> "F'"/5.6 = 7/4`
`=> "F'" = 7/4 xx 5.6`
`=> "F'" = 7 xx 1.4`
⇒ F' = 9.8 kg wt
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