A body weighs 5 kg on equator. At the poles it is likely to weigh

Options

A. 5 kg
B. less than 5 kg but not zero
C. 0 kg
D. more than 5 kg

Explanation

To determine the weight of a body at the poles when it weighs 5 kg at the equator, we can follow these steps:

### Step 1: Understand the Weight Formula
The weight \( W \) of an object is given by the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.

### Step 2: Identify the Mass
The mass of the body is constant and does not change with location. Given that the body weighs 5 kg at the equator, we can find the mass:
\[ W_{\text{equator}} = 5 \, \text{kg} \]
Since weight is a force, we should clarify that the weight in Newtons (N) is actually:
\[ W = m \cdot g \]
where \( g \) at the equator is approximately \( 9.78 \, \text{m/s}^2 \).

### Step 3: Calculate the Mass
To find the mass \( m \):
\[ m = \frac{W_{\text{equator}}}{g_{\text{equator}}} = \frac{5 \, \text{kg}}{9.78 \, \text{m/s}^2} \]
This calculation gives us the mass in kilograms.

### Step 4: Determine the Gravitational Acceleration at the Poles
The acceleration due to gravity \( g \) is slightly higher at the poles than at the equator due to the Earth's shape (it is an oblate spheroid). At the poles, \( g_{\text{pole}} \) is approximately \( 9.83 \, \text{m/s}^2 \).

### Step 5: Calculate the Weight at the Poles
Now we can calculate the weight of the body at the poles using the mass we found and the gravitational acceleration at the poles:
\[ W_{\text{pole}} = m \cdot g_{\text{pole}} = m \cdot 9.83 \, \text{m/s}^2 \]
Substituting the value of \( m \) we calculated earlier will give us the weight at the poles.

### Step 6: Conclusion
Since the gravitational acceleration is greater at the poles, the weight of the body will be more than 5 kg.

### Final Answer
The body will weigh more than 5 kg at the poles.

---