Gravitation

Question 1

g variation with theta

Answer 1

g’ = g - Rw^2cos^2(theta)

Question 2

g with h

Answer 2

g’ = g/(1 + h/R)^2

g’ = g/(1-2h/R)

Question 3

g with d

Answer 3

g’ = g(1-d/R)

Question 4

Potential inside solid sphere

Answer 4

g = GM (3R^2 - r^2)/2R^3

Question 5

Time period of planet in terms of R

Answer 5

T = 2pi root(R/g)

Question 6

Areal velocity = ?

Answer 6

L/2m = (1/2) rv sintheta

Question 7

vmax =? vmin = ?

Answer 7

root(GM/a (1+e)/(1-e))

root(GM/a (1-e)/(1+e))

Question 8

v< vo path?

Answer 8

elliptical with earth centre as focus

Question 9

vo < v < ve

Answer 9

ellipse with earth centre as focus

Question 10

v > ve

Answer 10

body escapes with hyperbola path

Question 11

v = ve

Answer 11

Body escapes with parabola path

Question 12

v = vo

Answer 12

Path is circular with earth centre as centre