Question

(a) An object has mass of 20 kg on earth. 
What will be its (i) mass, and (ii) weight, on the moon?(g on moon = 1.6 m/s^2).

(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 × 10^22 kg and a radius of 1.74 × 10^6 m (G = 6.7 × 10 -11Nm^2/kg^2). ​

Answer 1

Solution :-

(a) i) Mass on the moon = 20 Kg

ii) Weight on the moon = m

G moon= 20 × 1.6 = 32 N

(b) Say, G sat is the Acceleration due to Gravity on the Surface of the Satellite.

Then, G sat

= GM/r²

= (6.7 × 10 ^ -11 x 7.4 × 1022) / (1.74 × 106)²

= 1.63 m/s²

[ We get the eqn. of g sat in this way: weight of an object of mass m on the satellite is mg sat. The gravitational force on that mass m due the satellite of M is GMm/r²,

where r is the radius of the satellite.

Weight of the Object on Satellite = Gravitational Force on the Object due to the Satellite

mg sat = GM m/r²

g sat = GM/r² ]