Question

The linear density ρ in a rod 5 m long is 9/sqr(x+4) kg/m,  where x is measured...

The linear density ρ in a rod 5 m long is 9/sqr(x+4) kg/m,  where x is measured in meters from one end of the rod. Find the average density ρave of the rod.

Homework Answers

Answer #1

The given linear density function is,

The average density is given by,

integrate wrt x,


I hope this answer helps,
Thanks,
Keep posting questions.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A 1.00-m–long straight rod is manufactured to have a smoothly increasing linear mass density, so that...
A 1.00-m–long straight rod is manufactured to have a smoothly increasing linear mass density, so that at one end, it is 20.0 g/cm, and at the other end, it is 100 g/cm. (a) Assuming you place the low-mass-density end at x = 0, write the equation for the linear mass density of the rod as a function of x. (b) Use your answer from part (a) to determine the total mass of the rod. (c) Use your answers from parts...
A long thin rod of length L has a linear density λ(x)= A(L-x)^2 where x is...
A long thin rod of length L has a linear density λ(x)= A(L-x)^2 where x is the distance from the left end of the rod. a) What is the mass of the bar? b) How far is the center of mass of the bar from the left end of the bar?
An infinitely long, uniformly charged straight line has linear charge density ?1 coul/m. A straight rod...
An infinitely long, uniformly charged straight line has linear charge density ?1 coul/m. A straight rod of length 'b' lies in the plane of the straight line and perpendicular to it, with its enared end at distance 'a' from the line. The charge density on the rod varies with distance 'y', measured from the lower end, according to ?(on rod) = (?2*b)/(y+a), where ?2 is a constant. Find the electrical force exerted on the rod by the charge on the...
A long thin rod lies on the x axis with one end at the origin and...
A long thin rod lies on the x axis with one end at the origin and the other at the 4 cm point. It has a uniform linear charge density of 125 nano C/m. Find the E field due to this rod at the 52 cm position on the x axis. Find the force exerted by the rod on a point charge of 5 micro coulombs placed at a position of 109 cm on the x axis if the rod...
The total mass of a variable density rod is given by where m = mass, ρx=...
The total mass of a variable density rod is given by where m = mass, ρx= density, Ac(x)= cross-sectional area, x= distance along the rod, and L= the total length of the rod. The following data have been measured for a 20m length rod. Determine the mass in grams to the best possible accuracy. x,m 0 2 4 6 8 10 12 14 16 18 20 ρ, g/cm2 4.00 3.98 3.95 3.89 3.80 3.74 3.6 3.55 3.41 3.37 3.30 Ac,...
A thin rod sits along the xx axis with one end at x= -1.4 m and...
A thin rod sits along the xx axis with one end at x= -1.4 m and the other end at x= 3.5 m. The rod has a non-uniform density that increases linearly from 1.1 kg/m at the left end to 3.0 kg/m at the right end a What is the total mass of the rod? answer 10 kg b Where is the center of mass of the rod located? find it
The linear density (lamda) of a thin rod varies with position x as (lamda)=lamda0(x^3/L^3). The rod...
The linear density (lamda) of a thin rod varies with position x as (lamda)=lamda0(x^3/L^3). The rod lies along the X axis. If M is the mass of the rod and L is the total length, then, a) Find lamda0 in terms of M and L b)Find the position of the centre of mass c)Find the moment of inertia around the centre of mass. d) Now imagine the same thin rod is attached to a hinge that is allowed to rotate....
A 3m beam has two ends A and B. Its linear density varies. At a point...
A 3m beam has two ends A and B. Its linear density varies. At a point x meters away from end A, its linear density is given by the expression x^3 kg/m. a. What is the total weight of this beam? b. What is its average density? c. Where is the center of mass relative to the ends A and B?
Consider a rod that is 0.220 cm in diameter and 1.50 m long, with a mass...
Consider a rod that is 0.220 cm in diameter and 1.50 m long, with a mass of 0.0400 kg. 1. Find the moment of inertia about an axis perpendicular to the rod and passing through one end.(kg*m^2 units please) 2. Find the moment of inertia about an axis along the length of the rod. Express your answer in kilogram meters squared.
A rod of length 10 meters and charge .6 μC lies along the x-axis from (-5,...
A rod of length 10 meters and charge .6 μC lies along the x-axis from (-5, 0) to (5, 0) meters. A charge of .4 μC is placed at (0, 3) meters. a) Find the electric potential energy of the system if the rod has a uniform charge density. b) Find the energy if the rod has a linear charge density given by λ = kx2. c) Find the answer to (a) and (b) if the .4 μC charge was...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT