Question
The length of the rod is 10m and the measure of the linear density at a point is a linear function of the measure of the distance of the from the left end of the rod. The linear density at the left is 2kg/m and at the right end is 3kg/m. Find the total mass of the given rod and the center of the mass
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps

Knowledge Booster
Similar questions
- Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 1.20 1028 kg and 1.60 103 m. (a) Find the density of such a star.(b) If a dime (V = 2.0 10-7m3) were made from this material, how much would it weigh (in pounds)?arrow_forwardAn automobile tire is shown in the figure below. The tire is made of rubber with a uniform density of 1.10 × 103 kg/m³. The tire can be modeled as consisting of two flat sidewalls and a tread region. Each of th sidewalls has an inner radius of 16.5 cm and an outer radius of 30.5 cm as shown, and a uniform thickness of 0.675 cm. The tread region can be approximated as having a uniform thickness of 2.50 cm (that i its inner radius is 30.5 cm and outer radius is 33.0 cm as shown) and a width of 19.4 cm. What is the moment of inertia (in kg m2) of the tire about an axis perpendicular to the page through its center? " 33.0 cm 16.5 cm Sidewall 30.5 cm Tread Enter a number. find the moment of inertia of the sidewall and the moment of inertia of the tread region. Each can be modeled as a cylinder of nonzero thickness. What is the inner and outer radius for each case? What is the formula for the moment of inertia for a thick-walled cylinder? How can you find the mass of a hollow cylinder?…arrow_forward(D) The density of alumınum is 2.70 alam. Recal that density is mass divided bu uolume.lwhat is the mass of a cube m that is B.104cm on a Side in SI units. ot aluminur Express your answerarrow_forward
- Consider a cylinder of radius 40 cm and 60 cm high. Find the cylinder's volume in cubic feet.arrow_forwardAn oil circulates through a pipe (SG = 0.85), if the speed of the oil is 20 m / s and the diameter of the pipe is 10 cm, determine the mass flow of the oil (in Kg / s) in the pipe.arrow_forwardWhy is the average density not a "good" measure of density in this experiment? Mass (kg) Volume(m^3) Density (kg/m^3) 1.16 0.001 1160 2.46 0.0023 1069.565217 5.16 0.005 1032 10.16 0.01 1016 13.66 0.0135 1011.851852 Its a good measure The average does not account for the human errors in the measurements. The average does not account for the random errors in the measurements. The average does not account for the systematic errors in the measurements.arrow_forward
- The density of platinum is 21500 kg/m3 and that of aluminum is 2702 kg/m3. Find the ratio of the volume of 1.20 kg of platinum to the volume of 1.01 kg of aluminum.arrow_forwardthe average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom. What is the approximate density, in kilograms per cubic meter, of a nucleus?arrow_forwardThe effect of surface tension on the mass of a falling drop is studied. According to Raleigh for non-viscous flow the mass of a drop, ma, is a function of the surface tension, σ, the diameter of the droplet, d, the gravity, g, and the flow density, p. ma = f(d,g,p,σ) Find the relevant dimensionless numbers.arrow_forward
- Consider a water tank that is being filled with rainfall at the top and is drained through a small hole atthe bottom. The change in volume can be modelled by considering the amount of water entering andleaving the tank (per unit of time) as followsdVdt= fin − fout.Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout isin litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.(a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t andthat the tank is losing 10% of its volume of water per hour, such that, fout(V ) = 0.1V . Check bydirect substitution that the functionV (t) = 10(t + 5e−0.1t)satisfies the ODE and the initial condition.Now assume that the hole is slowly growing in size, so that the flow rate out increaseswith time:fout(V, t) = 0.1(1 + 0.1t)V.Solve the ordinary differential equation for V (t) with this flow rate out, using either separation…arrow_forwardWhat mass of fresh water (in kg) can be contained in a box whose dimensions are 270 mm by 257 mm by 468 mm? (Density of fresh water = 1000 kg/m^3)arrow_forward
arrow_back_ios
arrow_forward_ios