Calculate the centripetal acceleration on the equator on the earth. The radius of earth is 6 . 4 × 10 6 m and it completes one rotation in one day about its axis.

The earth is rotating about its axis in 24 hrs = 24 × 60 × 60 seconds and completing the rotation of angular displacement equal to 2 π The angular velocity of the earth = total angle of rotation time taken = 2 π 24 × 60 × 60 rad / sec . The centripetal acceleration = a c = ω 2 R = 2 π 24 × 60 × 60 2 6 . 4 × 10 6 = 3 . 4 × 10 - 2 ms - 2

IN hydrogen atom, an electron revolve around the proton at a speed of 2 . 18 × 10 6 m / s in a circle of the radius 5 . 28 × 10 - 11 m . Calculate the acceleration of electron and compare with acceleration due to gravity.

The radial acceleration of electron around the proton in hydrogen is a = v 2 r = 2 . 18 × 10 6 2 5 . 28 × 10 - 11 = 9 . 0 × 10 22 ms - 2 Where v , r are the velocity of the electron and the radius of the path respectably The value of acceleration due to gravity is g = 9 . 8 m / s 2 Comparing the two a g = 9 . 0 × 10 22 9 . 8 ≡ 10 22

In a hydrogen atom, an electron revolves around the proton in a circle of the radius 0 . 528 A ˙ . with a speed of 2 . 18 × 10 6 m / s . Calculate the centripetal force on the electron. (Mass of electron = 9 . 1 × 10 - 31 kg )

Given the path of the circular motion = 0 . 528 × 10 10 m Speed of the electron = 2 . 18 × 10 8 m / s The centripetal force on a body is given by F = mv 2 r , where m = mass of the body, v = velocity of the body and r = is the radius of the orbit. Substituting the values we have, F = 9 . 1 × 10 - 31 × 2 . 18 × 10 6 2 0 . 528 × 20 - 10 = 2 . 2 × 10 - 8 N