Conform/help with calc solution

[allenmatt59]

Homework Statement

Newton’s law of gravitation states that the force between two masses m1
and m2 at a distance r apart is F = Gm1m2/r2 .
(a) Find the magnitude of the gravitational force exerted by a solid hemisphere
of radius a and constant density  on a point mass located at
the center of the base of the hemisphere.
(b) A particle of mass m is placed at the center of one base of a circular
cylindrical shell of inner radius r1, outer radius r2, height h, and
constant density . Find the force of gravitational attraction exerted
by the cylinder on the particle.

The Attempt at a Solution

because the only force which would act on the bottom center of the hemisphere is pointed straight down. the force would be represented in a negative direction (-x/||x||). therefore f(x)=-mMGx/||x3||. ||x||=sqrt(x2+y2+z2).
because the force is coming only from the z direction F(x,y,z)=-mMGz/((z2)to the 3/2power)
is there someone to conform that.
and please lead me to the b part

thanks

 

[mighty2000]

for your post. I can confirm that your formula for the gravitational force exerted by a solid hemisphere is correct. The negative sign indicates that the force is attractive, pulling the point mass towards the center of the hemisphere.

For the second part, we can use a similar approach. The force of gravitational attraction between the particle and the cylindrical shell will be in the negative z direction, since the force is pulling the particle towards the center of the cylinder. The formula for this force would be F(x,y,z)=-mMGz/((z2)to the 3/2power).

To solve for the magnitude of the force, we can use the formula for the volume of a cylinder (V=πr2h), along with the given densities, to find the masses of the cylinder and the particle. Then, we can plug these values into the above formula to calculate the force of gravitational attraction between the two objects.

I hope this helps. Let me know if you have any further questions.