Title 4. GRAVITATION WS-2 (99-107).pmd.pdf ✅

VIII – Physics (Vol – III) Olympiad Class Work Book P O R d 2 GM g= R 4 3 but M = ρ πR 3       Where ρ is density of earth. 4πGρR g = (1) 3      The radius of effective mass of earth at a depth d is ( R-d ) Then d 4πGρ(R-d) g = (2) 3      From (1) & (2) d d g =g 1- R       Thus as depth increases, the acceleration due to gravity decreases Fractional change in ‘g’ Δg d = g R The variation of ‘g’ with distance from the centre is given below. g r=0 r=R r max g g r  2 1 g r 
Olympiad Class Work Book VIII – Physics (Vol – III) Variation of ‘g’ with latitude: Consider an object of mass “m” placed at latitude  of the earth as shown in figure. Due to rotation of earth, the value of acceleration due to gravity ( g  ) at that place changes.   P F F cos R The normal reaction at that place is given by N=mg-Fcosλ (Where F is centrifugal force) | mg =mg-Fcosλ -------(1) 2 F=mrω cosλ r = R cos λ 2 2 F=mRω cos λ ---------(2) 2 2 λ Rω g =g 1- cos λ g       Variation of ‘g’ with shape: The earth is elliptical in shape it flattened at the poles and bulged at the equa- tor so radius at equator is grater that the radius at poles. The value of ‘g’ at the equator is minimum and the poles is maximum. Lines joining the places on the earth having same value of “g” are called “ isogonic lines”