Answer: 17.83 AU
Explanation:
According to Kepler’s Third Law of Planetary motion <em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”. </em>
(1)
Talking in general, this law states a relation between the <u>orbital period</u> 
of a body (moon, planet, satellite, comet) orbiting a greater body in space with the <u>size</u> 
of its orbit.
However, if is measured in <u>years</u>, and is measured in <u>astronomical units</u> (equivalent to the distance between the Sun and the Earth: 
), equation (1) becomes:
(2)
This means that now both sides of the equation are equal.
Knowing 
and isolating from (2):
![a=\sqrt[3]{T^{2}}=T^{2/3}](https://tex.z-dn.net/?f=a%3D%5Csqrt%5B3%5D%7BT%5E%7B2%7D%7D%3DT%5E%7B2%2F3%7D)
(3)
(4)
Finally:
(5)
Answer:
h = 13.06 m
Explanation:
Given:
- Specific gravity of gasoline S.G = 0.739
- Density of water p_w = 997 kg/m^3
- The atmosphere pressure P_o = 101.325 KPa
- The change in height of the liquid is h m
Find:
How high would the level be in a gasoline barometer at normal atmospheric pressure?
Solution:
- When we consider a barometer setup. We dip the open mouth of an inverted test tube into a pool of fluid. Due to the pressure acting on the free surface of the pool, the fluid starts to rise into the test-tube to a height h.
- The relation with the pressure acting on the free surface and the height to which the fluid travels depends on the density of the fluid and gravitational acceleration as follows:
P = S.G*p_w*g*h
Where, h = P / S.G*p_w*g
- Input the values given:
h = 101.325 KPa / 0.739*9.81*997
h = 13.06 m
- Hence, the gasoline will rise up to the height of 13.06 m under normal atmospheric conditions at sea level.
Answer: True.
Explanation:
A resistance force is also known as friction. And the efficiency of a machine is affected by friction.
A machine of lower efficiency has higher magnitude of friction than a machine of higher efficiency.
Therefore, To obtain the same resistance force, a greater force must be exerted in a machine of lower efficiency than in a machine of higher efficiency. This is true
The motion of the ball on the vertical axis is an accelerated motion, with acceleration
The following relationship holds for an uniformly accelerated motion:
where S is the distance covered, vf the final velocity and vi the initial velocity.
If we take the moment the ball reaches the maximum height (let's call this height h), then at this point of the motion the vertical velocity is zero:
So we can rewrite the equation as
from which we can isolate h
(1)
Now let's assume that
is the initial velocity of the first ball. The second ball has an initial velocity that is twice the one of the first ball:
. So the maximum height of the second ball is
(2)
Which is 4 times the height we found in (1). Therefore, the maximum height of ball 2 is 4 times the maximum height of ball 1.
"A pitcher throws a baseball, and then the batter hits a homerun" is the one among the following choices given in the question that <span>best represents potential energy being converted to kinetic energy. The correct option among all the options that are given in the question is the second option or option "2". </span>
