Question

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Answer 1

Answer:

Mass of planet B is two times of mass of planet A .

Explanation:

Given-----> Radius of planet A is half the radius of planet B and value of g on B is half that of its value on A .

To find-----> Mass of B .

Solution-----> We know that ,

g = G m / r²

Here we have two planet A and B .

Let radius , mass and gravitational acceleration of planet A and B be r₁ , m₁ ,g₁ and r₂ , m₂ , g₂ respectively .

ATQ, Radius of planet A is half the radius of planet B

R₁ = R₂/2

=> 2 R₁ = R₂

Value of g on B is half that of its value on A

g₂ = g₁ / 2

=> G m₂ / R₂² = ( G m₁ / R₁² ) ( 1 / 2 )

G is cancel out from both sides , we get,

=> m₂ / R₂² = m₁ /2 R₁²

By cross multiplication , we get,

=> 2m₂ R₁² = m₁ R₂²

Putting R₂ = 2R₁ , in it we get,

=> 2 m₂ R₁ ² = m₁ ( 2R₁ )²

=> 2 m₂ R₁² = m₁ ( 4 R₁² )

R₁² cancel out from both sides , we get,

=> 2 m₂ = 4 m₁

=> m₂ = 4m₁ / 2

=> m₂ = 2m₁

So mass of planet B is two times of mass of planet A .