A solid sphere having uniform charge density `rho` and radius R is
How To Find Density Of A Sphere - How To Find. So find volume then divide mass by volume and there you go. Δρ/ρ = δm/m + 3δr/r homework equations δρ/ρ = δm/m + 3δr/r d = m/v the attempt at a solution i'm going to assume you use the radius and calculate the volume of a sphere (4/3pi(r^3), and then convert to m^3.
A solid sphere having uniform charge density `rho` and radius R is
Substituting in ρ = k r, i am left with. Give an expression for the constant k in terms of m and r. With the computed volume, this formula then executes the simple equation below to. Therefore, ρ = m 4 3 π r 3 = 3 m 4 π r 3. About press copyright contact us creators advertise developers terms privacy policy & safety how youtube works test new features press copyright contact us creators. In practice, it’s usually easier to measure diameter (d) and use the expression v = (1/6)πd^3. Ρ is defined as density, meaning ρ = m v o l u m e. To calculate the density of a sphere, determine its mass, then measure its radius and use the expression (4/3)πr^3 to find its volume. The formula for its volume equals: Ρ = m v where ρ is density in g/ml if mass m is in g and volume v is in ml.
We know that the density of this hollow sphere is f(r), so the mass of the hollow sphere is 4πr2f(r)δr. Volume of a sphere = 4 3 π r 3. Strategy once you know the volume, you can multiply by the density to find the mass. We are dealing with the surface area of the spherical balloon, not its volume. K r = 3 m 4 π r 3. If the gravitational field vector is independent of the radial distance within a sphere, find the function describing the mass density ρ ( r) of the sphere. We know that the density of this hollow sphere is f(r), so the mass of the hollow sphere is 4πr2f(r)δr. ∇ ⋅ g → = 4 π g ρ g = − g m r ^ r 2. Once you have the volume, look up the density for the material the sphere is made out of and convert the density so the units are the same in both the density and volume. (use the correct number of significant figures. After you've done this, you can plug the cubed radius into the original equation for calculating the volume of a sphere, v = ⁴⁄₃πr³.