The gravitational field intensity at a location X, in space, is two-fifths of its value on the earth’s surface. If the weight of an object at X is 4.80N. what is its weight on the earth?
Let's assume the weight of the object on Earth is W.
We know that the gravitational field intensity on Earth's surface is g. Thus, the gravitational field intensity at location X is (2/5)g.
The weight of an object is given by the formula W = mg, where m is the mass of the object and g is the gravitational field intensity.
So, the weight of the object at X is (2/5)g * m = 4.80N.
Since the weight on Earth is W = mg, we can equate the two equations:
mg = (2/5)g * m
W = (2/5)g * m
We can cancel out the mass (m) from both sides of the equation:
W = (2/5)g * m
W = (2/5)g * (1/m) * W
Now we can solve for W:
W = (2/5)g * (1/m) * W
5 * W = 2 * g * (1/m) * W
5 = 2 * g * (1/m)
Multiplying both sides of the equation by (1/g), we get:
(1/g) * 5 = 2 * (1/g) * g * (1/m)
5/g = 2 * (1/m)
5/g = 2/m
Multiplying both sides of the equation by m, we get:
5 * m/g = 2
m/g = 2/5
Now we can substitute this value back into the equation W = mg:
W = (2/5)g * m
W = (2/5)g * (g * (2/5))
W = (2/5) * g^2 * (2/5)
W = (4/25) * g^2
Therefore, the weight of the object on Earth is (4/25) * g^2.