I think the answer will be A
Kinetic energy = (1/2) (mass) (speed)²
The rock's kinetic energy is not
(1/2) (4 kg) (10 m/s)²
= (1/2) (4 kg) (100 m²/s²)
= 200 Joules .
It may be more, or it may be less. The only thing
we can be sure of is that it is not 200 Joules.
Answer:
5 years
Explanation:
The centripetal acceleration of a planet is equal to the acceleration due to gravity.
ac = g
Centripetal acceleration is:
ac = v² / r
where v is velocity and r is radius of travel.
Acceleration due to gravity is:
g = GM / r²
where G is gravitational constant, M is the mass of the sun, and r is the radius of travel.
Therefore:
v² / r = GM / r²
v² = GM / r
v = √(GM / r)
Distance is speed times time, so:
d = v t
2πr = √(GM / r) t
t = 2πr √(r / (GM))
t = 2π √(r³) / √(GM)
We know that when r = 1 AU, t = 1 year.
1 = 2π √(1³) / √(GM)
1 = 2π / √(GM)
2π = √(GM)
Substituting:
t = 2π √(r³) / (2π)
t = √(r³)
When r = 3AU:
t = √(3³)
t = 5.2
Planet B takes approximately 5 years to orbit the sun.
Answer:
The acceleration of the centre of mass of spool A is equal to the magnitude of the acceleration of the centre of mass of spool B.
Explanation:
From the image attached, the description from the complete question shows that the two spools are of equal masses (same weight due to same acceleration due to gravity), have the same inextensible wire with negligible mass is attached to both of them over a frictionless pulley; meaning that the tension in the wire is the same on both ends.
And for the acceleration of both spools, we mention the net force.
The net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.
For this system, the net force on either spool is exactly the same in magnitude because the net force is a difference between the only two forces acting on the spools; the tension in the wire and their similar respective weights.
With the net force and mass, for each spool equal, from
ΣF = ma, we get that a = ΣF/m
Meaning that the acceleration of the identical spools is equal also.
Hope this Helps!
The period of Neptune is 165 years if the semi-major axis is 30.11 using the given formula.
Answer: Option D
<u>Explanation:
</u>
The period of any planet revolutions around the sun can be determined using Kepler third law. As that law states that square to the period of one complete revolution of every planet is equal to cube of semi major axis of that planet. So the formula can be derived as
Where T is the time taken for completing one revolution and a is the semi-major axis of the planet.
As here Neptune's semi major axis is given as 30.11. So the period of Neptune can be determined as follows:
Then take square root of this value:
T = 165 years
Thus, the Neptune takes 165 years for one complete revolution of the sun.