Question

If the earth suddenly stops rotating, then the weight of an object of mass $m$ at the equator will [$\omega$ is the angular speed of the earth and $R$ is its radius ] :

• A. decreases by $m{\omega }^{2}R$
• B. increase by $m{\omega }^{2}R$
• C. decrease by $m\omega R^2$
• D. increase by $m\omega R^2$

Answer 1

The correct option is B

increase by $m{\omega }^{2}R$

Step 1: Given Data

Mass $=m$

The angular speed of the earth $=\omega$

Radius of earth $=R$

Let $g$ be the acceleration due to gravity.

Step 2: Formula Used

Acceleration due to gravity at the latitude $\lambda$ is given by

$g_{\lambda }=g-R{\omega }^2{\cos }^2\lambda$

Step 3: Calculate the Accelerations

Acceleration due to gravity at the latitude $\lambda$ is given by

$g_{\lambda }=g-R{\omega }^2{\cos }^2\lambda$

At equator, $\lambda =0°$

Under normal conditions, the acceleration due to gravity at the equator is given as,

$g_e=g-R{\omega }^2$

When the earth stops rotating $\omega =0$.

Therefore, the new acceleration due to gravity at the equator is given as,

$g_e\text{'}=g-0=g$

$\therefore g_e<g_e\text{'}$

Step 4: Calculate the Change in Weight

Therefore the change in weight is given as,

$$\begin{gathered} △W=\left(g_e\text{'}-g_e\right)m \\ =\left(g-g+R{\omega }^2\right)m \\ =m{\omega }^{2}R \end{gathered}$$

Hence, if the earth suddenly stops rotating, then the weight of an object will increase by $m{\omega }^{2}R$, and therefore the correct answer is option (B).