Find the magnitude of the gravitational field

[matt_crouch]

Homework Statement

Find the magnitude of the gravitational field a distance r from an infinitly long uniform thin rod whose mass per unit length is (lamda)

Homework Equations

The Attempt at a Solution

Need some clarification really
i know

dgx=-Gdm/r²

r=r₂-r₁

lamda=m/L

i substituded them in and intergrated

so to finally get

=-GM/r₂²-r₁²

 

[kuruman]

You need to show the details of what you did. Otherwise it is hard to figure out what you did wrong. However, your final answer must be in terms of lambda r and G. There should be no M (the mass of the rod is infinite) or r₁ and r₂ (there is only one r, the distance of the point of interest to the rod).

 

[kerimek]

I would first clarify the units of the given mass per unit length (lambda) to ensure that the units are consistent with the gravitational constant G. Then, I would explain that the gravitational field is a vector quantity and its magnitude can be calculated using the equation:

g = -G * (lambda / r)

where G is the gravitational constant, lambda is the mass per unit length, and r is the distance from the rod. This equation can be derived by considering the gravitational force between a small section of the rod and a mass at distance r from it.

The integral approach taken in the attempt at a solution is also valid, as the gravitational field can be calculated by integrating the contributions from each small section of the rod. However, the limits of integration and the substitution of r2-r1 for r may need further clarification. Additionally, the negative sign in the equation should be taken into account as it indicates the direction of the gravitational field.