Question

if the radii of 2 planets be r1 and r2 ,their mean densiyies be d1 and d2, then prove that thr rstio of acceleration due to gravity on the palnets will be r1d1:r2d2​

Answer 1

Answer:

let seg AB and seg CD represent the two two plants seg BD represent the road

Answer 2

Answer:

Explanation:

Volume of 1st planet, V1 = (4/3) pi r13

Mass of 1st planet, M1 = (4/3) pi r13 d1

Therefore, Acceleration due to gravity of the first planet, a1 = [(4/3) pi r13 d1 * G] /r12 = (4/3) pi r1 d1 * G​

Again, Volume of 2st planet, V2 = (4/3) pi r23

Mass of 2st planet, M2 = (4/3) pi r23 d2

Therefore, Acceleration due to gravity of the second planet, a2 = [(4/3) pi r23 d2 * G] /r22 = (4/3) pi r2 d2 * G​

A/Q

a1 : a2 = [(4/3) pi r1 d1 * G​​] : [(4/3) pi r2 d2 * G​]

         = r1 d1 : r2 d2.        

                                              Therefore, it is proved.