Final answer:
The weight of the stone on the heavenly body is 399.5312 N.
Step-by-step explanation:
The weight of an object depends on the mass of the object and the acceleration due to gravity. In this case, the heavenly body has a mass equal to half of the mass of the earth and its radius is half as that of the earth. We can use the formula for weight:
Weight = mass x acceleration due to gravity
Let's assume the mass of the stone on earth is 'm'. The weight of the stone on earth is given as 100N. The acceleration due to gravity on earth is approximately 9.8 m/s^2.
So, 100 = m x 9.8. Solving for 'm', we find the mass of the stone on earth as 10.2041 kg.
Now, since the heavenly body has half the radius and its gravitational force is directly proportional to the mass and inversely proportional to the square of the radius, the weight of the stone on the heavenly body will be:
Weight on heavenly body = (mass of stone)x (acceleration due to gravity on heavenly body)
Let's denote the mass of the heavenly body as 'M' and the acceleration due to gravity on the heavenly body as 'g'. Since the heavenly body has half the radius of the earth, the acceleration due to gravity on the heavenly body will be four times greater than on earth (because g is inversely proportional to the square of the radius).
Thus, the weight of the stone on the heavenly body will be:
Weight on heavenly body = 10.2041 kg x (4x9.8 m/s^2) = 399.5312 N