Question

The mass of Jupiter is 314 times that of Earth and diameter of the Jupiter is 11.35 times of Earth. If g = 9.8 ms -2 on Earth, find its value on Jupiter.

Answer 1

accl due to gravity of any planet is given by: (GM)/(R^2). where G= universal gravitational constant, M= mass of that planet, R = radius of that planet.
hence gravity on earth :
9.8=(G×M)/(R^2) ............(1)
where M is mass of earth and R is radius of earth.
further,
it is given,
mass of Jupiter=314M,
radius of Jupiter= 11.35R,
then gravity at Jupiter(g') is given by:
g' = (G×314×M)/(11.35R×11.35R)
= 2.43×[(GM)/(R^2)]
from equation (1) putting value of (GM)/(R^2) we get,
g'= 2.43×9.8=23.88m/s^2.

Answer 2

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Distance of Jupiter from the Earth, D = 824.7 × 106 km = 824.7 × 109 m

Angular diameter=35.72" = 35.72 × 4.874 × 10^-6 rad

Diameter of Jupiter = d

Using the relation,

θ = d/D

=> d = D θ = 824.7 × 10^9 × 35.72 × 4.874 × 10^-6

= 1.435 × 10^5 km

I hope, this will help you

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