IIT (NTSE/Olympiad)  


The relation between the mass of earth, comparison of messes of two planets and value of a gravity calculation of satellite with different formulas are used.

(1) Relation between mass of earth and its density :

(2) Mass of Earth (Me) :
Me = = 6.6 x 1024 kg (approx.)
(3) Value of 'g' on other planets :

(4) Comparison of masses of two planets :

where T1 = Time period of Ist planet.
T2 = Time period of IIndplanet.
r1 = Orbital radius of Ist planet.
r2 = Orbital radius of IInd planet.
(5) Mass of Sun :

where T = Time period of Earth = 365 days & r = Distance of earth form sun.
(6) If we throw a body from earth towards moon, then as body moves away from the surface of earth the value gearth decreases, as a result the weight (W = mg on earth) decreases. At a particular height gearth = gmoon therefore W = 0. Now above this height gmoon becomes effective and weight (W) increases till body reaches, at the surface of the moon.
(7) If two mass m and M moves towards each other due to gravitational force, from rest, then relative velocity of approach will be, where r is separation between masses.
(8) Maximum height attained by a projectile (h) is given by : h =
(9) If h1 is the maximum height attained by a man on a planet whose acceleration due to gravity is g1 and h2 is the maximum height attained on a planet whose acceleration due to gravity is g2 then. g1h1 = g2h2
(10) On clock based on spring, the effect of acceleration due to gravity is negligible but on pendulum based clock effect of 'g' is noticed if 'g' increases, time period decreases and the clock moves fast if 'g' decreases time period increases and the clock moves slow.
(11) Work done in changing the orbit of satellite :
W = Change in total energy =

(12) If satellite is moved to higher orbit then potential energy, angular momentum, increases but kinetic energy, binding energy, orbital velocity, decrease.

IIT (Class X)