The weight of spaceman speff at the surface of planet x, solely due to its gravitational pull, is 389 n. if he moves to a distance of 1.86 × 104 km above the planet's surface, his weight changes to 24.31 n. what is the mass of planet x, if speff's mass is 75.0 kg? (g = 6.67 × 10-11 n · m2/kg2)

Answer

given,

W = weight of speff at surface of planet = 384 N  

h= height = 1.86 x 10⁴ Km

W' = weight of speff at height h from the planet = 24.31 N

Ms = speff mass = 75 kg

M= mass of planet = ?  

R = radius of planet

G = 6.67 x 10⁻¹¹ m³/kg.s²

g = 5.187 m/s²

we know,

.......(1)

now,

g' = 0.324 m/s²

.........(2)

dividing equation (1)/(2)

r = 6.2 x 10⁶ m

mass of planet X

from equation 1

M = 3.21 x 10²⁴ kg

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach