JEE Class main Answered

Let M be mass of earth , R be the radius of earth and G is universal gravitational constant .

If the particle is projected with speed      at a distance r from center of earth , then it revolves around the earth in circular motion

of radius r so that the gravitational force of attraction equals centripetal force. Hence we get

....................... (1)

By substituting in above equation and after simplification, we get

r = 2R

if T is time period of revolution of particle , then we have

.........................(2)

By substituting v_o from eqn.(2) and after simplification , we get from eqn.(1) as

.............................(3)

we know that when r = 2R , time period of revolution is T

Hence if if time period of revolution is 8T , then distance r of particle from center of earth is obtained from eqn.(3) as

r = (2R) × 4 = 8R

Hence n = 8

-----------------------------------------------------------------