If earth suddenly stop rotating , then the weight of an object of mass m at equator will [ `omega ` is angular speed of earth and R is its radius . ]

Options

A. Decrease by `momega^(2)R`
B. Increase by `momega^(2)R`
C. Decrease by `momegaR^(2)`
D. Increase by `m omega R^(2)`

Answer

To solve the problem of what happens to the weight of an object of mass \( m \) at the equator if the Earth suddenly stops rotating, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Weight**:
The weight \( W \) of an object is given by the formula:
\[ W = mg \]
where \( g \) is the acceleration due to gravity.

2. **Effect of Earth's Rotation**:
While the Earth is rotating, the effective acceleration due to gravity \( g' \) at the equator is reduced due to the centrifugal force acting outward. The effective gravity can be expressed as:
\[ g' = g - R\omega^2 \]
where \( R \) is the radius of the Earth and \( \omega \) is the angular speed of the Earth.

3. **When Earth Stops Rotating**:
If the Earth suddenly stops rotating, the angular speed \( \omega \) becomes zero. Thus, the effective acceleration due to gravity at the equator becomes:
\[ g' = g - R(0)^2 = g \]

4. **Weight Calculation Before and After**:
- Before stopping, the weight of the object at the equator is:
\[ W' = mg' = m(g - R\omega^2) \]
- After stopping, the weight of the object becomes:
\[ W = mg \]

5. **Comparison of Weights**:
Since \( g' < g \), the weight of the object when the Earth is rotating is less than when it is not rotating. Therefore, the weight increases when the Earth stops rotating.

6. **Change in Weight**:
The change in weight \( \Delta W \) can be calculated as:
\[ \Delta W = W - W' = mg - m(g - R\omega^2) = mR\omega^2 \]
This shows that the weight of the object increases by \( mR\omega^2 \) when the Earth stops rotating.

### Conclusion:
Thus, the weight of the object of mass \( m \) at the equator will increase by \( mR\omega^2 \) if the Earth suddenly stops rotating.