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]
3 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]3 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
4. What type of assessments are based on repeatable, measurable data?
Harman [31]

Answer:

  • OBJECTIVE ASSESSMENTS
  • SUBJECTIVE ASSESSMENTS
  • BODY COMPOSITION ASSESSMENTS
  • COGNITIVE ASSESSMENTS

Explanation:

PLS MAKE ME BRAINLIEST

8 0
2 years ago
Trình bày về Thí nghiệm tán xạ Rutherford, phát hiện proton.
Setler [38]

Answer:

Any other language I don't know this language

6 0
3 years ago
qual o nome da posição que o planeta tem maior velocidade? este ponto é mais próximo ou mais afastado do sol?
klio [65]

Em inglês, esse ponto é 'perihelion' ... 'periélio'. É o mais próximo que a Terra ou o planeta chega do sol.

7 0
3 years ago
Calculate the gravitational potential energy of a 2 kg banana hanging 5
Hunter-Best [27]

Answer:

  100 J

Explanation:

The potential energy is given by the formula ...

  PE = mgh

  = (2 kg)(10 m/s^2)(5 m) = 100 J

7 0
3 years ago
• 2. A 70 kg man on a 100 kg boat throws a ball. The boat moves backwards 5 meters in 10 seconds. What is
Kipish [7]

Answer:

0.5 m/sec

Explanation:

v=S÷t

 =5÷10

v=0.5 m/sec

6 0
3 years ago
Other questions:
  • How does the electric potential energy change as the electron moves from i to f?
    12·1 answer
  • In most cases, a multicellular organism is not an exact copy of its parents because it
    10·2 answers
  • A gas has an initial volume of 212 cm3 at a temperature of 293 K and a pressure of 0.98 atm. What is the final pressure of the g
    14·2 answers
  • Can somebody help me with this
    7·1 answer
  • If the weight of an object of mass "m" is "mg," then the weight of an object of mass "2m" is
    13·2 answers
  • A 0.22 kg air track glider moving at 0.60 m/s a collides elastically into a 0.44 kg glider at rest. After collision the 0.22 kg
    14·1 answer
  • A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is
    12·1 answer
  • An electromagnetic wave of wavelength 435 nm is traveling in vacuum in the —z direction. The electric field has an amplitude of
    10·1 answer
  • A good easy question for a science minded person!! 20 points for whoever answer
    11·1 answer
  • Which of the following occurs during the evolution of a star?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!