Question

A sphere of radius R has total mass M and density function given by ρ = kr, where r is the distance a point lies from the centre of the sphere. Give an expression for the constant k in terms of M and R.

Answer #1

A sphere with radius 0.150 m has density ρ that decreases with
distance r from the center of the sphere according to
ρ=3.25×103kg/m3−(8.50×103kg/m^4)r .
a)Calculate the total mass of the sphere. Express your answer
with the appropriate units.
B)Calculate the moment of inertia of the sphere for an axis
along a diameter. Express your answer with the appropriate
units.

A sphere with radius 0.250 m has density ρ that decreases with
distance r from the center of the sphere according to
ρ=2.75×103kg/m3−(9.00×103kg/m4)r . Part A: Calculate the total mass
of the sphere. Express your answer with the appropriate units. M =
?; Try Again Part B :Calculate the moment of inertia of the sphere
for an axis along a diameter. Express your answer with the
appropriate units.

A solid non-conducting sphere of radius R has a
nonuniform charge distribution of volume charge
density ρ = rρs/R, where ρs
is a constant and r is the distance from the
centre of the sphere.
Show that:
(a) the total charge on the sphere is Q = π
ρsR3 and
(b) the magnitude of the electric field inside the
sphere is given by the equation
E = (Q r2 /
4π ε0R4)

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
(a) The new sphere has density ρ = ρ0 and mass M >
M0
(b)...

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Options: R F U R or U F or U R or F or U
The...

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Read it to me
The new sphere has radius R > R0 and density ρ...

A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Options are:
R= Rises
F= Falls
U= Unchnaged
F or U
R or U
F...

3. Consider a solid hemisphere of radius R, constant mass
density ρ, and a total mass M. Calculate all elements of the
inertia tensor (in terms of M and R) of the hemisphere for a
reference frame with its origin at the center of the circular base
of the hemisphere. Make sure to clearly sketch the hemisphere and
axes positions.

A small solid sphere of mass M0, of radius R0, and of uniform
density ρ0 is placed in a large bowl containing water. It floats
and the level of the water in the dish is L. Given the information
below, determine the possible effects on the water level L,
(R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a
new solid sphere of uniform density. The new sphere has density ρ =
ρ0 and radius R > R0 The new...

A solid, homogeneous sphere with a mass of m0, a radius of r0
and a density of ρ0 is placed in a container of water. Initially
the sphere floats and the water level is marked on the side of the
container. What happens to the water level, when the original
sphere is replaced with a new sphere which has different physical
parameters? Notation: r means the water level rises in the
container, f means falls, s means stays the same....

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