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
stepladder [879]
3 years ago
5

Q.By the method of dimensional analysis derive the

Physics
2 answers:
Alchen [17]3 years ago
5 0

Answer:

LHS=RHS=[L]

Two identical spheres of which one  is solid and other hollow take different times to descend an  inclined plane because of their different mass distribution about the center of rotation.

Explanation:

Given mathematical expression:

where:                                             dimension:

s = displacement length                [L]

u = initial velocity                           [L.T^{-1}]

t = time                                                 [T]

a = acceleration                             [L.T^{-2}]

now using dimensional analysis:

LHS=[L]

and

RHS=[L.T^{-1}]\times [T]+[L.T^{-2}]\times [T]^2

we know that the ratio and constants have no dimension.

\Rightarrow RHS=[L]

∵LHS=RHS

As we know that only similar dimensions can be added or subtracted therefore we get a correct conclusion.

However we can deduce the operators between the equations and can neither check for the validity of the constants. We can only check for the dimension of the terms involved.

2)

Two identical spheres of which one  is solid and other hollow take different times to descend an  inclined plane because of their different rolling motion.

we know that:

  • the moment of inertia of a solid sphere is given as, I=\frac{2}{5} m.R^2
  • the moment of inertia of a hollow sphere is given as, I=\frac{2}{3} m.R^2

Torque during the rolling would be given as:

\tau=I.\alpha

\Rightarrow \alpha=\frac{\tau}{I}

This indicates that the solid sphere will descend first when other parameters remain constant.

Artyom0805 [142]3 years ago
4 0

Answer

a) Using dimensional analysis we cannot derive the relation, But we can check the  correctness of the formula.

  s = u t +\dfrac{1}{2}at^2

now,  L H S

  s = distance

  dimension of distance = [M⁰L¹T⁰]

now, equation on the right hand side

 R H S

 u = speed

 u = m/s

 Dimension of speed = [M⁰L¹T⁻¹]

dimension of time

  t = sec

 Dimension of time = [M⁰L⁰T¹]

 Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]

                              = [M⁰L¹T⁰]

now, acceleration= a

  a = m /s²

dimension of acceleration = [M⁰L¹T⁻²]

dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]

                              = [M⁰L¹T⁰]

hence, the dimension are balanced.

so, L H S = R H S

b) Moment of inertia of hollow sphere = \dfrac{2}{3}Mr^2

  Moment of inertia of solid sphere = \dfrac{2}{5}Mr^2

   we know,

    \tau = I \alpha

    \alpha=\dfrac{\tau}{I}

Torque is the force that causes rotation

If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.

Thus the solid sphere would accelerate more.

You might be interested in
If the mass of the ladder is 12.0 kgkg, the mass of the painter is 55.0 kgkg, and the ladder begins to slip at its base when her
Marysya12 [62]

Answer:

 μ = 0.336

Explanation:

We will work on this exercise with the expressions of transactional and rotational equilibrium.

Let's start with rotational balance, for this we set a reference system at the top of the ladder, where it touches the wall and we will assign as positive the anti-clockwise direction of rotation

          fr L sin θ - W L / 2 cos θ - W_painter 0.3 L cos θ  = 0

          fr sin θ  - cos θ  (W / 2 + 0,3 W_painter) = 0

          fr = cotan θ  (W / 2 + 0,3 W_painter)

Now let's write the equilibrium translation equation

     

X axis

        F1 - fr = 0

        F1 = fr

the friction force has the expression

       fr = μ N

Y Axis

       N - W - W_painter = 0

       N = W + W_painter

       

we substitute

      fr = μ (W + W_painter)

we substitute in the endowment equilibrium equation

     μ (W + W_painter) = cotan θ  (W / 2 + 0,3 W_painter)

      μ = cotan θ (W / 2 + 0,3 W_painter) / (W + W_painter)

we substitute the values ​​they give

      μ = cotan θ  (12/2 + 0.3 55) / (12 + 55)

      μ = cotan θ  (22.5 / 67)

      μ = cotan tea (0.336)

To finish the problem, we must indicate the angle of the staircase or catcher data to find the angle, if we assume that the angle is tea = 45

       cotan 45 = 1 / tan 45 = 1

the result is

    μ = 0.336

5 0
3 years ago
A SMALL cup of tea has water inside that is very hot, about 80 degrees Celsius. A LARGE bathtub has water inside it that is warm
Artist 52 [7]

Answer:

the water in the tea cup

Explanation:

Kinetic energy is the energy an object or particles possesses as a result of motion.

Liquid in higher temperature possesses more kinetic energy than liquid with lower temperature

7 0
3 years ago
g A lighter ball A with momentum PA=5.0 kg∙m/s in positive x-direction approaches a heavier ball B at rest before the collision.
Svet_ta [14]

Answer:

7kgm/s

Explanation:

Using the law of conservation of momentum which states that the sum of momentum of bodies before collision is equal to the sum of the bodies after collision.

Let P1A and P1B be the initial momentum of the bodies A and B respectively

Let P2A and P2B be the final momentum of the bodies A and B respectively after collision.

Based on the law:

P1A+P2A = P1B + P2B

Given P1A = 5kgm/s

P2A = 0kgm/s(ball B at rest before collision)

P2A = -2.0kgm/s (negative because it moves in the negative x direction)

P2B = ?

Substituting the values in the equation gives;

5+0 = -2+P2B

5+2 = P2B

P2B = 7kgm/s

3 0
3 years ago
Why is it important to study electromagnetic waves?
labwork [276]
The study of EM is essential to understanding the properties of light, its propagation through tissue, scattering and absorption effects, and changes in the state of polarization. ... Since light travels much faster than sound, detection of the reflected EM radiation is performed with interferometry.
3 0
3 years ago
what is the potential energy of the ball when it gets to its maximum height just before falling back to the ground​
love history [14]

Answer:

I will say that the the potential energy will be at its maximum.

Explanation:

potential energy deals with gravity and gravity deals with height, so when a object is in its maximum height it will have the maximum potential energy.  

6 0
3 years ago
Other questions:
  • A ball at rest starts rolling down a hill with a constant acceleration of 3.2 meters/second. What is the final velocity of the b
    15·1 answer
  • Why is density and the melting point both substances of mass
    6·1 answer
  • Tennis is classified as an exercise program. Please select the best answer from the choices provided. T F
    11·2 answers
  • a proton is fired with a speed of 200,000m/s from the midpoint of the capacitor toward the positive plate. This speed is insuffi
    9·2 answers
  • An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use your futuristic dual electric/m
    11·1 answer
  • What is the relationship between frequency and degree of refraction?
    10·1 answer
  • In the diagram, the arrow shows the movement of electric
    14·1 answer
  • Friction always opposes ___________ motion​
    7·1 answer
  • A 1.23 x 10^3 kilogram car is traveling east at 25 meters per second. The brakes are applied and the car is brought to rest in 5
    7·1 answer
  • Identify the vibrating media in three different types of musical instruments
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!