Suppose a planet exists whose mass and radius both are half those of earth
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whats your question tell it nicely
Suppose a planet exists whose mass is twice the Earth’s with a radius 3 times greater. What is the weight of an object of mass 10 kg on its surface?
On Earth, 10kg weighs 10kg x 9.8m/s^2 = 98N.
The equation to use is F = G(m1)(m2)/r^2…
On Earth, 98N = G(Mearth)(10kg)/r^2, where G is the gravitational constant, Mearth is the mass of Earth, 10kg is our object, and r is the radius of the Earth.
The only things changing are the mass of the planet - at twice Earth’s, and it’s radius, which is 3 times Earth’s… so:
Fplanet = G(2Mplanet)(10kg)/(3r)^2. G is the same, 10kg is the same, so call them some constant K.
Fearth = K(Mearth)/r^2 = 98N; if r = 1 and Mearth = 1, then K = 98
Fplanet = K(2Mearth)/(3r)^2
Fplanet = 98(2/9) = 196/9 = 21.78N