2FI8(Dimensional Analysis) The gravitational force of attraction F between two objects dependson the masses m1 and m2 of the two objects, the distance r between the two objects, and thegravitational constant G. Here are the units, using kg for kilograms, m for meters, and sec forseconds:2.[F] = kg m/sec2[m2] = kg[m,] kg[r] m[G] m3/(sec2 kg)(а.)Find a dimensionless group involving F, G, m1, m2, and r. In doing this, assume thatthe exponents on mi and m2 are the same.(ь.)Use your result in part (a.) to find a dimensionally feasible formula for thegravitational force of attraction F. Assume that the II number is 1.The gravitational force is said to be an inverse square law involving the distancebetween the two objects. Does your formula(c.)with this?agreeWhat happens to the gravitational force of attraction if the distance between two(d.)objects is doubled? Be specific.

Question
Asked Nov 6, 2019
25 views
2FI8
(Dimensional Analysis) The gravitational force of attraction F between two objects depends
on the masses m1 and m2 of the two objects, the distance r between the two objects, and the
gravitational constant G. Here are the units, using kg for kilograms, m for meters, and sec for
seconds:
2.
[F] = kg m/sec2
[m2] = kg
[m,] kg
[r] m
[G] m3/(sec2 kg)
(а.)
Find a dimensionless group involving F, G, m1, m2, and r. In doing this, assume that
the exponents on mi and m2 are the same.
(ь.)
Use your result in part (a.) to find a dimensionally feasible formula for the
gravitational force of attraction F. Assume that the II number is 1.
The gravitational force is said to be an inverse square law involving the distance
between the two objects. Does your formula
(c.)
with this?
agree
What happens to the gravitational force of attraction if the distance between two
(d.)
objects is doubled? Be specific.
help_outline

Image Transcriptionclose

2FI8 (Dimensional Analysis) The gravitational force of attraction F between two objects depends on the masses m1 and m2 of the two objects, the distance r between the two objects, and the gravitational constant G. Here are the units, using kg for kilograms, m for meters, and sec for seconds: 2. [F] = kg m/sec2 [m2] = kg [m,] kg [r] m [G] m3/(sec2 kg) (а.) Find a dimensionless group involving F, G, m1, m2, and r. In doing this, assume that the exponents on mi and m2 are the same. (ь.) Use your result in part (a.) to find a dimensionally feasible formula for the gravitational force of attraction F. Assume that the II number is 1. The gravitational force is said to be an inverse square law involving the distance between the two objects. Does your formula (c.) with this? agree What happens to the gravitational force of attraction if the distance between two (d.) objects is doubled? Be specific.

fullscreen
check_circle

Expert Answer

Step 1

(a) The number of  dimensional variables are 5 namely, F, G, m1, m2 and r. The reference dimensions are M, L, T. Thus, according to the Buckingham Pi theorem, the number of non-dimensional variables are 5-3=2.

Step 2

Choose r and m2 as the repeating variables.

Find the first non-dimensional group

help_outline

Image Transcriptionclose

InFGmr MET =(MLT*) (MET2) (M)Y (L)

fullscreen
Step 3

Solve for the e...

help_outline

Image Transcriptionclose

a-b+c 0 a+3b+1-0 -2a-2b 0 -FGmp

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Advanced Physics

Related Advanced Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: A metallic ring of crossection 2.5 cm^2 mean radius 40 cm and relative permeability 1500 is wound un...

A: The metallic ring is wound uniformly of wire. As a result, it is a toroid.

question_answer

Q: A charge of -6.00 nC is spread uniformly over the surface of one face of a nonconducting disk of rad...

A: The surface charge density of the circular disc is

question_answer

Q: 3. An RLC Circuit is governed by the differential equation d21 R dl +I-0 dt2 L dt LC where I(t) give...

A: (a)Write the given differential equation and plug 0 for R, we get

question_answer

Q: (10%) Problem 8: An infinite solid insulating cylinder of radius R and has a uniform volume charge d...

A: An infinite solid insulating cylinder of radius R and has a uniform volume charge density 1.3 µC/m2....

question_answer

Q: Consider a series RLC circuit which is driven by an AC applied voltage. At resonance A. the curren...

A: Here, the capacitor will nullify the effect of inductor. Hence, the current is in phase with the dri...

question_answer

Q: what is the speed of light

A: The speed of light in vacuum is 299792458 m/s.Most commonly the speed of light in vacuum is approxim...

question_answer

Q: A football is kicked from ground level with an initial velocity given by  v0x = 20.0 m/s  and  v0y =...

A: Write the expression for the maximum height

question_answer

Q: Physical Chemistry  What is the maximum number of phases that can be in mutual equilibrium in a 2 co...

A: Consider the number of components be C, the degree of freedom be F, that is equivalent to zero in mu...

question_answer

Q: 3E0, and uHo) and for two 4. For uniform plane wave propagation in (i) ice (o 106 S/m, 8 (ii) seawat...

A: Write the expression for attenuation constant, phase constant, wavelength, skin depth and velocity