Question

The rotation of the earth about its axis speeds up such that a man on the equator becomes weightless. In such a situation, what would be the duration of one day?

• A. 2π
• B. $\frac { 1 } { 2 \pi } \sqrt { \frac { R } { g } }$
• C. 2π$\sqrt { \operatorname { Rg } }$
• D. $\frac { 1 } { 2 \pi } \sqrt { \mathrm { Rg } }$

Answer 1

Answer: (A)

2π

Answer 2

Let ω = angular velocity of the earth about its axis.

mg – N = mω²R

for N = 0, ω² = g/R.

T = $\frac { 2 \pi } { \omega } = 2 \pi \sqrt { \frac { \mathrm { R } } { \mathrm { g } } }$ .