Respuesta :
The effect on the gravitational force if:
a. Both masses are multipled by 3: the gravitational force becomes 9 times.
b. The distance between centers is X4: the gravitational force gets reduced by 16 times.
c. One mass is X2 and the other X3 : the gravitational force becomes 6 times.
d. The distance is divided by 2: the gravitational force becomes 4 times.
e. The distance is divided by 2 and one mass X3: the gravitational force becomes 12 times.
We know that the gravitational force between two objects is given by,
F = Gm1m2 / r² ...........(1)
We need to find the effect on the gravitational force if
a. Both masses are multipled by 3
F1 = G(3m1)(3m2) / r²
F1 = 9 Gm1m2 / r²
F1 = 9F ...........(from equation (1))
Thus the gravitational force becomes 9 times.
b. The distance between centers is X4
F2 = Gm1m2 / (4r)²
F2 = Gm1m2 / 16r²
F2 = 1/16 ( Gm1m2 / r²)
F2 = 1/16 * F ...........(from equation (1))
Thus the gravitational force gets reduced by 16 times.
c. One mass is X2 and the other X3
F3 = G(2m1)(3m2) / r²
F3 = 6 * Gm1m2 / r²
F3 = 6F ...........(from equation (1))
Thus the gravitational force becomes 6 times.
d. The distance is divided by 2
F4 = Gm1m2 / (r/2)²
F4 = Gm1m2 / (r²/4)
F4 = 4 ( Gm1m2 / r²)
F4 = 4F ...........(from equation (1))
Thus the gravitational force becomes 4 times.
e. The distance is divided by 2 and one mass X3
F5 = G(3m1)m2 / (r/2)²
F2 = 3Gm1m2 / (r²/4)
F2 = (3*4) ( Gm1m2 / r²)
F2 = 12 F ...........(from equation (1))
Thus the gravitational force becomes 12 times.
Therefore, The effect on the gravitational force if:
a. the gravitational force becomes 9 times.
b. the gravitational force gets reduced by 16 times.
c. the gravitational force becomes 6 times.
d. the gravitational force becomes 4 times.
e. the gravitational force becomes 12 times.
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