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?

Answer 1

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.