in gravitational field, difference of gravitational potential between 2 points distant dr apart is dv. The intensity of field is.....???

a.dv*dr b.dv/dr c.dr/dv d. -dv/dr

To determine the intensity of a gravitational field based on the difference in gravitational potential between two points, we need to understand the relationship between gravitational potential and gravitational field intensity. The gravitational field intensity, often denoted as \( g \), is defined as the negative gradient of the gravitational potential \( V \). This means that the intensity of the gravitational field is related to how much the potential changes over a certain distance.

Understanding Gravitational Potential and Field Intensity

Gravitational potential \( V \) at a point in a gravitational field is the work done per unit mass to bring a small mass from infinity to that point. When we have two points that are a distance \( dr \) apart, the change in gravitational potential between these two points is denoted as \( dV \).

Mathematical Relationship

The intensity of the gravitational field \( g \) can be mathematically expressed as:

• g = -\frac{dV}{dr}

This equation indicates that the gravitational field intensity is equal to the negative rate of change of gravitational potential with respect to distance. The negative sign signifies that the gravitational field points in the direction of decreasing potential.

Analyzing the Options

Now, let’s evaluate the options you provided:

• a. \( dV \cdot dr \)
• b. \( \frac{dV}{dr} \)
• c. \( \frac{dr}{dV} \)
• d. \( -\frac{dV}{dr} \)

From our earlier discussion, we can see that option d, \( -\frac{dV}{dr} \), correctly represents the intensity of the gravitational field. The other options do not accurately reflect the relationship between gravitational potential and field intensity.

Conclusion

Thus, the correct answer to your question is option d: \( -\frac{dV}{dr} \). This relationship is fundamental in understanding how gravitational fields operate and how they influence objects within the field. If you have any further questions or need clarification on any part of this topic, feel free to ask!