The amount of heat needed to increase the temperature of a solid sphere of diameter 2D of the same metal from 4°C to 7°C is is 8 times the initial amount of heat.
<h3>What is heat?</h3>
The temperature increment will lead to the increase in the internal energy of the object. This internal energy is the heat.
Given is the change in temperature ΔT = 7-4 =3°C., diameter D to 2D,
Q = Cp x ρ(4π/3)D³ x 3..................(1)
and Q' = Cp x ρ(4π/3)(2D)³ x 3
Q' = Cp x ρ(4π/3)8D³x 3..................(2)
Dividing both the equation, we have
Q' / Q =8
Q' = 8Q
Thus, the amount of heat needed to increase the temperature of a solid sphere of diameter 2D of the same metal from 4°C to 7°C is 8 times the initial amount of heat.
Learn more about heat.
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To solve this problem, we use the Law of Universal Gravitation:
F = Gm1m2/d^2
where m1 and m2 are two objects. In this case, earth and man. d is the distance between the objects. Lastly, G is the gravitational constant. Since the mass of the earth and man are constant, this is lumped up with G into k. The equation would be:
F = k/d^2
k = Fd^2

The radius of earth, d1, is equal to 6.371E+6 m. Thus, d2 = 2d1
(8E+2)(d1)^2 = F2(2d1)^2
(8E+2)(d1)^2 = 4F2(d1)^2
(8E+2)=4F2
F2 = 200 Newtons