Respuesta :
Explanation:
(a) The given data is as follows.
M = 1100 kg, r = 5.01 mm = [tex]5.01 \times 10^{-3}[/tex] m
m = 2.40 kg
Now, formula for Newton's law of gravitation is as follows.
F = [tex]\frac{GMm}{r^{2}}[/tex]
Putting the given values into the above formula as follows.
F = [tex]\frac{GMm}{r^{2}}[/tex]
= [tex]\frac{6.673 \times 10^{-11} Nm^{2}/kg^{2} \times 1100 \times 2.40 kg}{(5.01 \times 10^{-3})^{2}}[/tex]
= [tex]7.02 \times 10^{-3}[/tex] N
Therefore, gravitational force exerted by the given sphere on 2.40 kg point mass is [tex]7.02 \times 10^{-3}[/tex] N.
(b) Now, mass of the sphere beyond r = 2.50 mm or [tex]2.50 \times 10^{-3} m[/tex] will not contribute any force on the point mass.
Hence, mass within the radius r < R that experiences force is,
[tex]m^{1} = M \frac{r^{3}}{R^{3}}[/tex]
According to Newton's law of gravitation,
F = [tex]\frac{Gm^{1}m}{r^{2}}[/tex]
= [tex]\frac{Gm(M \frac{r^{3}}{R^{3}})}{r^{2}}[/tex]
= [tex]G \frac{mMr}{R^{3}}[/tex]
Here, r is the radius of point mass and R is the radius of solid sphere.
Therefore, putting the given values into the above formula as follows.
F = [tex]G \frac{mMr}{R^{3}}[/tex]
= [tex]\frac{6.673 \times 10^{-11} Nm^{2}/kg^{2} \times 1100 kg \times 2.40 kg \times 2.50 \times 10^{-3}}{(5)^{3}}[/tex]
= [tex]3.52 \times 10^{-9}[/tex] N
Therefore, the gravitational force this sphere exerts on a 2.40 kg is [tex]3.52 \times 10^{-9}[/tex] N.
Gravitational force exerted on a 2.4 kg point mass placed
a) At 5.01 mm from the center of the sphere = 7.02 * 10⁻³ N
b) At 2.50 mm from the center of the sphere = 3.52 * 10⁻⁹ N
Given data :
Mass ( M ) = 1100 kg
Radius ( R ) = 5.00 m
point mass ( m ) = 2.40 kg
Gravitational constant = 6.673 * 10⁻¹¹
a) Gravitational force exerted at 5.01 mm from the center of the sphere
applying Newton's law of gravitation
r = 5.01 * 10⁻³ m
F = [tex]\frac{GMm}{r^{2} }[/tex] = ( 6.673 * 10⁻¹¹ * 1100 * 2.40 ) / ( 5.01 * 10⁻³ )²
= 7.02 * 10⁻³ N
B) Determine the gravitational force exerted at 2.50 mm from the center
Applying Newton's law of gravitation
r = 2.5 * 10⁻³ m
F = [tex]\frac{GMm}{r^{2} }[/tex] = ( 6.673 * 10⁻¹¹ * 1100 * 2.40 ) / ( 2.50 * 10⁻³ )²
= 3.52 * 10⁻⁹ N
Hence we can conclude that the Gravitational force exerted on a 2.4 kg point mass placed At 5.01 mm from the center of the sphere = 7.02 * 10⁻³ N At 2.50 mm from the center of the sphere = 3.52 * 10⁻⁹ N
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