Answer:
The force of gravity after you double the mass and the distance is half of the initial force: 
Explanation:
The initial force of gravity is:
where 
is the universal gravitational constant, 
is the mass of the first object, 
is the mass of the second object, and 
is the distance between the objects.
If the mass of the second object is doubled, now we have 
, and if the distance between the objects is also doubled instead of now we have 
.
So the force of gravity now is:
and we know that
so the new force of gravity is:
The force of gravity after you double the mass and the distance is half of the initial force.
Answer:
According to Kepler's 3rd law.
It states that the orbital period, T is related to the distance, r as:
T²
= 4
π²r³
/G M
where G is the universal gravitational constant = 6.673 × 10⁻¹¹ Nm²/kg²
Rearranging for M should give Jupiter's mass.
M =
4
π²r³/GT²
T= 1.77 days × 24 h/day × 60 min/h × 60 s/min = 1.53 × 10⁵ s
r = 4.22x10⁸ m
M = 4π² ((4.22 × 10⁸ m)³/(6.673 × 10⁻¹¹ Nm²/kg² x (1.53 × 10⁵ s)²)
M = 1.90 × 10²⁷kg
The mass of Jupiter is 1.90 × 10²⁷kg.
1.90 × 10²⁷kg
T= 7.16 days × 24 h/day × 60 min/h × 60 s/min = 6.19 × 10⁵s
r = 1.07x10⁹ m
M = 4π² ((1.07 × 10⁹ m)³/(6.673 × 10⁻¹¹ Nm²/kg² x (6.19 × 10⁵ s)²)
M = 1.90 × 10¹⁷kg
The mass of Jupiter is 1.90 × 10¹⁷kg.
THE RESULTS TO PART A and B ARE NOT CONSISTENT. The reason is because of the difference in radius of each satellites from Jupiter. i.e the farther away the moons, the smaller they become in space and the more the number of days to complete an orbit.
Answer- thermal energy :)
Answer:
The moment of inertia of the turntable about the rotation axis is 0.0225 kg.m²
Explanation:
Given;
radius of the turnable, r = 60 cm = 0.6 m
rotational kinetic energy, E = 0.25 J
angular speed of the turnable, ω = 45 rpm
The rotational kinetic energy is given as;
where;
I is the moment of inertia about the axis of rotation
ω is the angular speed in rad/s
Therefore, the moment of inertia of the turntable about the rotation axis is 0.0225 kg.m²
Answer:
(A) –14m/s
(B) –42.0m
Explanation:
The complete solution can be found in the attachment below.
This involves the knowledge of motion under the action of gravity.
Check below for the full solution to the problem.
