BITSAT2016PhysicsGravitationActual
What should be the velocity of rotation of earth due to rotation about its own axis so that the weight of a person becomes 3 5 of the present weight at the equator. Equatorial radius of the earth is 6400 ~km .
Options
- A8.7 10⁻⁷ rad / s
- B7.8 10⁻⁴ rad / s
- C6.7 10⁻⁴ rad / s
- D7.4 10⁻³ rad / s
Correct answer
B. 7.8 10⁻⁴ rad / s
Step-by-step solution
True weight at equator, W=m g Observed weight at equator, W ^ = mg ^ = 3 5 mg At equator, latitude =0 Using the formula, array l mg ^ = mg - mR ² ² 3 5 mg = mg - mR ² ² 0= mg - mR ² mR ²= mg - 3 5 mg = 2 5 mg = ( 2 5 g R )^ 1 / 2 = ( 2 9.8 5 6.4 10⁶ )^ 1 / 2 =7.8 10⁻⁴ rad / s array