1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesya692 [45]
2 years ago
10

A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ=cx2, where x is

measured from the center of the rod and c is a constant.A. What are the units of c?Mastering physics says the answer is: kg/m^3 but i don't understand where they got this answer.B. Find the expression for c.Mastering physics says the answer is 12M/L^3 --> No clue where they got this answer!C. Find the expression for the moment of inertia of the rod for rotation about an axis through the center.
Physics
1 answer:
grigory [225]2 years ago
4 0

Answer:

Explanation:

λ=c x²

c = λ / x²

λ is mass / length

so its dimensional formula is ML⁻¹

x is length so its dimensional formula is L

c = λ / x²

= ML⁻¹ / L²

= ML⁻³

B )

We shall find out the mass of the rod with the help of given expression of mass per unit length and equate it with given mass that is M

The mass in the rod is symmetrically distributed on both side of middle point.

we consider a small strip of rod of length dx at x distance away from middle point

its mass dm = λdx = cx² dx

By integrating it from -L to +L we can calculate mass of whole rod , that is

M = ∫cx² dx

= [c x³ / 3] from -L/2 to +L/2

= c/3 [ L³/8 + L³/8]

M = c L³/12

c = 12 M L⁻³

C ) Moment of inertia of rod

∫dmx²

= ∫λdxx²

= ∫cx²dxx²

= ∫cx⁴dx

= c x⁵ / 5 from - L/2 to L/2

= c / 5 ( L⁵/ 32 +L⁵/ 32)

= (2c / 160)L⁵

= (c / 80) L⁵

= (12 M L⁻³/80)L⁵

= 3/20 ML²

=

=

You might be interested in
A 25N force is acting on a body moving on a straight line with Initial momentum 20 kam's. Find the final momentum after 4 second
Nezavi [6.7K]

The final momentum of the body is equal to 120 Kg.m/s.

<h3>What is momentum?</h3>

Momentum can be described as the multiplication of the mass and velocity of an object. Momentum is a vector quantity as it carries magnitude and direction.

If m is an object's mass and v is its velocity then the object's momentum p is: {\displaystyle \mathbf {p} =m\mathbf {v} . The S.I. unit of measurement of momentum is kg⋅m/s, which is equivalent to the N.s.

Given the initial momentum of the body = Pi = 20 Kg.m/s

The force acting on the body, Pf = 25 N

The time, Δt = 4-0 = 4s

The Force is equal to the change in momentum: F ×Δt = ΔP

25 × 4 = P - 20

100 = P - 20

P = 100 + 20 = 120  Kg.m/s

Therefore, the final momentum of a body is 120 Kg.m/s.

Learn more about momentum, here:

brainly.com/question/4956182

#SPJ1

5 0
9 months ago
How to do this question
mestny [16]

thanks again and have to go to the store and get some rest I will be there at puno my phone is not working and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about you

4 0
2 years ago
Why is random sampling and random assignment in experimental research important?
Hunter-Best [27]

So the result is not biased or affected in some way

6 0
2 years ago
150c passes through cell in 30 seconds. cell has a potential difference of 12v. what is current in the circuit
zzz [600]

The current in the circuit is 5 A

Explanation:

The intensity of current is given by the equation:

I=\frac{q}{t}

where

I is the current

q is the amount of charge passing through a given point of the circuit in a time interval of t

For the cell in this problem, we have

q = 150 C is the charge

t = 30 s is the time interval

Substituting into the equation, we f ind

I=\frac{150}{30}=5 A

Learn more about current:

brainly.com/question/4438943

brainly.com/question/10597501

brainly.com/question/12246020

#LearnwithBrainly

6 0
3 years ago
True or false. The planet's speed never changes. That is why we have a stable orbit.
Svetradugi [14.3K]
This answer is true the earth always stays at one speed
8 0
1 year ago
Other questions:
  • One of the main arguments that animal rights advocates present is that animals have rights because they __________.
    9·2 answers
  • Two tuning forks, 254 Hz. and 260 Hz., are struck simultaneously. How many beats will be heard?
    9·1 answer
  • How long is the image of a metrestick formed by a plane mirror?
    7·1 answer
  • True or False: If your gas pedal jams, you should turn the key to lock to lock the steering wheel.
    8·2 answers
  • Describe how the gravitational force between 2 objects depends on the mass of the objects and the distance between them. your an
    13·1 answer
  • Compare relative age with absolute age.
    14·1 answer
  • A plane with the speed of 210 miles per hour is flying at an angle of 40 degrees from true east and a 45 mile per hour wind is b
    6·1 answer
  • A car goes East from 2 m/s to 16m/s in 3.5s. What is the Car's acceleration?
    11·1 answer
  • Consider the diagram of a pendulum's motion shown above. A pendulum can be used to model the change from potential energy
    6·1 answer
  • If an object accelerates from rest, with a constant acceleration of
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!