Doubt from gravitation

Question no 1,2 and 4

Please help anyone @Sneha_2021, @Prajwal_2020_1, @Achyut_2020

Is the answer 1 for 4

For 4th answer is option B

This is because the first and third law only depends on 1/r^2 of the gravitational force while the third law holds true for any central force.

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  1. Yes the earth did move towards the apple but the earths displacement is negligible as compared to apple's.

dA/dt = L/2m. L(angular momentum) of any planet about the sun is constant,as the force always acts towards the sun, thus making the torque due to gravitational force 0. This won't change even if the value of the force acting were to change. So, the area swept will always be constant for any planet in orbit.

For 1, the earth did move towards the apple, as did the apple move towards the earth's centre - the force acting on them is of the same magnitude. However, the earth has a very large mass, thus we get a very small acceleration, thus resulting in a really small, and thus, negligible movement.

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For 2, due to earth's rotation, all of us experience a centrifugal force(outwards), thus reducing the force to less than 'mg; . Since earth rotates about the line joining the two poles, the centrifugal force would be directly proportional to to the distance of the person from this line. However, if you stand at the poles, there would be no distance at all, and you would weigh exactly equal to 'mg'.

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Is answer to question 4 wrong i am getting as (5/4+1/root2)^(1/2) GM/L^2 but answer key says 2root2GM/L^2

Question no 9 and 10 also

Please help anyone

Question no 7,8th second and third part and question 9

Please help @Achyut_2020 , @Prajwal_2020_1

9 A as for shell we can take it at center

8 (2)as they are light so they have less attraction due to gravity ,so they have more tendency to escape

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For 7 apply energy conservation

For 9th Option B is correct given in answer key of shell question

Please help in 9 and 10th question in post 11 as i got different answers from given in answer key

For 9 is it D