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
Gelneren [198K]
3 years ago
5

The matter that makes up a planet is distributed uniformly so that the planet has a fixed, uniform density. How does the magnitu

de of the acceleration due to gravity g at the planet surface depend on the planet radius R ? (Hint: how does the total mass scale with radius?) g ∝ 1 / R g ∝ R g ∝ √ R g ∝ R 2
Physics
1 answer:
Trava [24]3 years ago
8 0

Answer:

the acceleration due to gravity g at the surface is proportional to the planet radius R (g ∝ R)

Explanation:

according to newton's law of universal gravitation ( we will neglect relativistic effects)

F= G*m*M/d² , G= constant , M= planet mass , m= mass of an object , d=distance between the object and the centre of mass of the planet

if we assume that the planet has a spherical shape,  the object mass at the surface is at a distance d=R (radius) from the centre of mass and the planet volume is V=4/3πR³ ,

since M= ρ* V = ρ* 4/3πR³ , ρ= density

F = G*m*M/R² = G*m*ρ* 4/3πR³/R²= G*ρ* 4/3πR

from Newton's second law

F= m*g = G*ρ*m* 4/3πR

thus

g = G*ρ* 4/3π*R = (4/3π*G*ρ)*R

g ∝ R

You might be interested in
A 7 kg sled is initially at rest on a horizontal road. the sled is pulled a distance of 2.9 m by a force of 42 n applied to the
Artemon [7]
I have no idea on this question.
6 0
3 years ago
The mass of a sample of iron is 31.5 g. The volume is 5 cm3. What is the density of iron in g/cm3?
ELEN [110]
Answer : 6.3 g/cm3
Step by step explanation:
Density = mass/volume
3 0
2 years ago
A proton, starting from rest, accelerates through a potential difference of 1.0 kV and then moves into a magnetic field of 0.040
Minchanka [31]

Answer:

r = 0.11 m

Explanation:

The radius of the proton's resulting orbit can be calculated equaling the force centripetal (Fc) with the Lorentz force (F_{B}), as follows:

F_{c} = F_{B} \rightarrow \frac{m*v^{2}}{r} = qvB (1)

<u>Where:</u>

<em>m: is the proton's mass =  1.67*10⁻²⁷ kg</em>

<em>v: is the proton's velocity</em>

<em>r: is the radius of the proton's orbit</em>

<em>q: is the proton charge = 1.6*10⁻¹⁹ C</em>

<em>B: is the magnetic field = 0.040 T </em>

Solving equation (1) for r, we have:

r = \frac{mv}{qB}   (2)

By conservation of energy, we can find the velocity of the proton:

K = U \rightarrow \frac{1}{2}mv^{2} = q*\Delta V   (3)

<u>Where:</u>

<em>K: is kinetic energy</em>

<em>U: is electrostatic potential energy</em>

<em>ΔV: is the potential difference = 1.0 kV </em>

Solving equation (3) for v, we have:

v = \sqrt{\frac{2q\Dela V}{m}} = \sqrt{\frac{2*1.6 \cdot 10^{-19} C*1.0 \cdot 10^{3} V}{1.67 \cdot 10^{-27} kg}} = 4.38 \cdot 10^{5} m/s  

Now, by introducing v into equation (2), we can find the radius of the proton's resulting orbit:

r = \frac{mv}{qB} = \frac{1.67 \cdot 10^{-27} kg*4.38 \cdot 10^{5} m/s}{1.6 \cdot 10^{-19} C*0.040 T} = 0.11 m

Therefore, the radius of the proton's resulting orbit is 0.11 m.

I hope it helps you!  

5 0
3 years ago
What is the formula for potassium iodide
musickatia [10]
Potassium iodide

Molar mass: 166.0028 g/mol

Formula: KI
3 0
3 years ago
Read 2 more answers
Part of understanding the physical effects on Mars, we must understand
Ber [7]

Answer:

so easy add the subtract then multiplay the add

Explanation:

8 0
3 years ago
Other questions:
  • Why does the cyclist have less kinetic energy at position A than at position B?
    6·1 answer
  • A car traveling at 27 m/s starts to decelerate steadily. It comes to a complete stop in 12 seconds. What is its acceleration?
    8·1 answer
  • A metal detector used in airports is actually a large coil of wire carrying a small current. Explain how it detects a gun, even
    10·1 answer
  • A geological process Select one: A. is limited to acting on rocks B. shapes and changes the earth C. starts in the outer atmosph
    8·1 answer
  • What happens during an equinox?
    10·1 answer
  • Half of the moon is always illuminated by the sun. Given that this is true, then what causes the moon to change phases throughou
    13·1 answer
  • A roller coaster is stopped on a track. When the engineer presses a launch button on the coaster, the coaster moves forward. Exp
    12·1 answer
  • A toy helicopter has a mass of .25 kg. The rotors of the helicopter exert an upward lift
    12·1 answer
  • Explain why a ball thrown in space could keep moving forever, while a ball thrown here on Earth will come to a stop.
    11·1 answer
  • What angle (in degrees) is needed between the direction of polarized light and the axis of a polarizing filter to cut its intens
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!