Planet in a space has a mass thrice that of the earth and a radius twice that of the earth.What will be the weight of a book on this planet,if its weight on the earth is 400N?

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Solution

$A c c e l e r a t i o n d u e t o g r a v i t y o n t h e e a r t h i s, g = 9.8 m / s^{2} \approx 10 m / s^{2} W e i g h t o n t h e e a r t h, W = m g 400 = m \times 10 S o, m = 40 k g A l s o g o n t h a t p l a n e t i n s p a c e g' = \frac{M' G}{R^{' 2}} G i v e n, M' = 3 M R' = 2 R S o, g' = \frac{3 M G}{4 R^{2}} g' = \frac{3}{4} g S o, W e i g h t o n t h a t p l a n e t m g' = 40 \times \frac{3}{4} \times 10 = 300 N$

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Planet in a space has a mass thrice that of the earth and a radius twice that of the earth.What will be the weight of a book on this planet,if its weight on the earth is 400N?

Acceleration due to gravity on the earth is ,g = 9.8 m/s2≈10 m/s2Weight on the earth ,W = mg400 = m×10So ,m = 40 kgAlso g on that planet in space g' = M' GR'2Given , M' = 3 M R' =2 RSo ,g' =3 MG 4R2g' = 34gSo , Weight on that planetmg' = 40×34×10 = 300 N