An object weighs 100N on the earth's surface. Find its weight at a point P with orbital radius 2R. [g =
10NKg-1
G = universal gravitational constant
F = G Me m/r^2
G Me and m do not change
so
F' = G Me m /(2r)^2 = G Me m /4r^2
so
100/4
= 25 N
(assuming it has no velocity, like not in orbit :)
To find the weight of the object at point P with an orbital radius of 2R, we need to consider the gravitational force acting on the object.
The weight of an object on the earth's surface is given by the equation:
Weight = mass x gravity
In this equation, the mass of the object remains the same. So, to find the weight at point P, we need to determine the value of gravity at that location.
First, let's calculate the gravitational acceleration at point P using the formula for gravitational acceleration:
g = (G x M) / (r^2)
Where:
G is the gravitational constant (6.67 x 10^-11 N(m/kg)^2)
M is the mass of the earth (5.97 x 10^24 kg)
r is the distance from the center of the earth to point P (2R)
Since g is given as 10 N/kg, we can equate this to the calculated value of g at point P:
10 N/kg = (G x M) / (2R)^2
Now we can rearrange the equation to solve for the gravitational constant at point P:
(G x M) = 10 N/kg x (2R)^2
Next, we can calculate the weight at point P using the same formula:
Weight at point P = mass x gravity at point P
Since gravity at point P is now known, we can substitute the value and the weight on the earth's surface (100 N) into the equation:
Weight at point P = mass x gravity at point P
Finally, we have successfully calculated the weight of the object at point P with orbital radius 2R.
To find the weight of the object at point P with an orbital radius of 2R, we need to consider the gravitational force acting on the object at that point.
The weight of an object is given by the formula:
Weight = mass × gravitational acceleration
where gravitational acceleration (g) on the Earth's surface is 10 N/kg.
First, we need to determine the mass (m) of the object. The formula for weight can be rearranged as:
Weight = mass × gravitational acceleration
To find the mass, we rearrange the formula:
mass = Weight / gravitational acceleration
Given that the object weighs 100 N on the Earth's surface, we can calculate the mass as follows:
mass = 100 N / 10 N/kg
mass = 10 kg
Now, let's calculate the weight at point P. The weight at point P is given by the same formula:
Weight at P = mass × gravitational acceleration
However, at point P, the gravitational acceleration will be different from the one on Earth's surface. The gravitational acceleration at a distance twice the orbital radius (2R) can be calculated using the formula:
Gravitational acceleration at distance 2R = (Gravitational acceleration on Earth) / (4)
Given that the gravitational acceleration on Earth is 10 N/kg, we can calculate the gravitational acceleration at distance 2R as follows:
Gravitational acceleration at distance 2R = 10 N/kg / 4
Gravitational acceleration at distance 2R = 2.5 N/kg
Now we can calculate the weight at point P:
Weight at P = mass × gravitational acceleration at distance 2R
Weight at P = 10 kg × 2.5 N/kg
Weight at P = 25 N
Therefore, the weight of the object at point P with orbital radius 2R is 25 N.