Question

Note: I need question 11 to be done mustly. then after that if you can please answer the MCQS

11. The gravitational field intensity at a height of 150 km (1.50 x 102 km) above the surface of Uranus is 8.71 N/kg. The radius of Uranus is 2.56 x 107m. la) Calculate the mass of Uranus. b) Calculate the gravitational field intensity at the surface of Uranus. lc) How much would a 100 kg (1.00 x 102 kg) person weigh on the surface of Uranus?

MCQS

Answer 1

11. (a) Let M be the mass, R be the radius and h be the height above the surface of Uranus, then,

Gravitational field = GM/(R+h)² ,

Where, G = 6.67*10^-11 Nm²/kg² is universal gravitation constant, h = 150 km = 0.015*10⁷ m,

Thus, 8.71 = 6.67*10^-11M/(2.56+0.015)²*10¹⁴

Or, 8.71 = M*1.0059*10^-25

Or, M = (8.71*10²⁵/1.0059)

Thus, mass of Uranus = 8.67*10²⁵ kg

(b) Gravitational field intensity at the surface of Uranus will be

= GM/R²

  = (6.67*10^-11*8.67*10²⁵/2.56²*10¹⁴)

= 8.82 N/kg

(c) Weight of the person on the surface of Uranus will be

W = Mass*Field intensity at the surface

= (100*8.82) N

= 882 N