Gravitation

Question 1

Intensity I =

Answer 1

GM/r^2

Question 2

For solid sphere I =

Answer 2

GMr/R^3

Question 3

Acc due to gravity g

Answer 3

GM/R^2 (at surf)

Question 4

At height h, g` =

Answer 4

g/(1+h/R)^2
if h«R, g` = g(1-2h/R)

Question 5

At depth d, g` =

Answer 5

g(1-d/R)

Question 6

At center, d =

Answer 6

R

Question 7

Due to rotation of earth, g` =

Answer 7

g - ω^2Rcos^2λ

Question 8

For solid sphere, V =

Answer 8

V(out) = -GM/r
V(on) = -GM/R
V(in) = -GM(3R^2 - r^2)/2R^3

Question 9

Hollow sphere, V

Answer 9

V(out) = -GM/r
V(surf) = -GM/R
V(in) = -GM/R

Question 10

Escape speed V(e) =

Answer 10

√2GM/R

Question 11

Orbital velocity for satellites

Answer 11

V(o) = √GM/r

Question 12

KE =

Answer 12

GMm/2r

Question 13

PE =

Answer 13

-2KE