the ratio of acc due to gravity at a depth h below the surface of earth and at a height h above the surface of earth h << radius of earth
(A) is constant
(b) increases linearly with h
(c) increases parabolically with h
(d) decreases
49the options are confusing!!
i go for decreases with increase in h!!
but still the value approximately remains the same for h<<R
30Option b and c are redundant because value of g is maximum at the surface of the Earth..
I feel it should be option d) decreases
that is when h<<R,
g'=g(1 - h/R)
1Acc due to grav blow earths surface at depth 'h'= gb=g ( 1- h/R) and above ga=g (1-2h/R). Ratio gb/ga =(1-h/R) (1-h/2R)-1. Since h<<R therefore considering only the first term of the expansion we get( 1- h/R) (1+ h/2R).This gives 1- h/R + 2h/R - 2h2/R2. Neglecting the higher powers of h/R and simplifying we get 1+ h/R. This quantity will increase linearly with 'h'. So (b) is correct
30my mistake..I didnt read the question properly.. Yes.. Agree with sengupta..
49!!!! ohh!!
this thing (the soln by sengupta) boggled my mind!! :P
1while calculating gravitational force b/n extended objects can we consider their mass to be concentrated at their centre of masses.
suppose i'm calculating Fg b/n a point mass and rod
0 --------------------------------------------------
m M, length L
and let distence b/N them be d.
Then, after performing integration Fg comes out to be GMm/d(d+L)
BUT, IF WE WOULD HAVE ASSUMED MASS TO BE COMCENTRATED AT ROD'S CENTRE
Fg should have been GMm/(d+L/2)^2
SO, WHATS XRONG IN THE ASSUMPTION....
