David lands on planet X and observes objects free-falling withacceleration 4.9 m

Question

David lands on planet X and observes objects free-falling withacceleration 4.9 m/s2 . If the planet is 4 times larger than theEarth, what is the planet MASS expressed in Earth masses? Please give step by step instrustios with solution for 10points David lands on planet X and observes objects free-falling withacceleration 4.9 m/s2 . If the planet is 4 times larger than theEarth, what is the planet MASS expressed in Earth masses? Please give step by step instrustios with solution for 10points Please give step by step instrustios with solution for 10points

Explanation / Answer

Let the mass of planet X be M The acceleration due to gravity on the planet X is a =4.9 m/s2 The mass of the planet X is R = 4r,where r isthe radius of Earth The acceleration of gravity at the Earth's surface is g = G * (m/r2) -------------------(1) Here,G is the universal gravitational constant and m is themass of Earth.The value of g is 9.8 m/s2. Similarly,the acceleration of gravity at the surface of planetX is a = G * (M/R2) or a = G * (M/(4r)2) = (1/16) * G *(M/r2) ------------------(2) The mass of the planet X is R = 4r,where r isthe radius of Earth The acceleration of gravity at the Earth's surface is g = G * (m/r2) -------------------(1) Here,G is the universal gravitational constant and m is themass of Earth.The value of g is 9.8 m/s2. Similarly,the acceleration of gravity at the surface of planetX is a = G * (M/R2) or a = G * (M/(4r)2) = (1/16) * G *(M/r2) ------------------(2) Dividing equation (1) by equation (2),we get (g/a) = [G * (m/r2)/(1/16) * G *(M/r2)] or (g/a) = (Gm/r2) * (16r2/GM) =(16m/M) or M = 16m * (a/g) or M = 16m * (4.9/9.8) = 8m Therefore,the mass of the planet X is eight times the mass ofEarth.

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