Q5 of 15 Page 14

Solve the following example.

The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value on A?

We know that acceleration due to gravity (g) is given by


Where G = universal gravitational constant;


M = mass of the planet;


R = radius of the planet;


Mass of Planet A = MA;


Radius of Planet A = RA;


Value of ‘g’ on A = gA;



Mass of Planet B = MB;


Radius of Planet B = RB;


Value of ‘g’ on B = gB;



Also it is given that;






Therefore;







(from question )


⇒


Therefore the mass of planet B should be two times the mass of planet A i.e MB = 2MA .


More from this chapter

All 15 →
4

Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be √8 T.

 5

Solve the following example.

An object takes 5 s to reach the ground from a height of 5 m on a planet. What is the value of g on the planet?

 5

Solve the following example.

The mass and weight of an object on earth are 5 kg and 49 N respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is 1/6th of that on the earth.

 5

Solve the following example.

An object thrown vertically upwards reaches a height of 500 m. What was its initial velocity? How long will the object take to come back to the earth? Assume g = 10 m/s2