two lead spheres whose diameters are 20 cm and 2 cm are placed with centres 100 cm apart. Calculate the force of gravitation between them.(density of lead =11500 kg/m^3
To calculate the force of gravitation between the two lead spheres, you can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where:
F is the force of gravitation,
G is the gravitational constant (approximately 6.674 * 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two lead spheres, and
r is the distance between their centers.
To find the masses of the lead spheres, we need to know their volumes first. The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
Let's calculate the volume and mass of each sphere:
For the first sphere:
Radius (r1) = diameter / 2 = 20 cm / 2 = 10 cm = 0.1 m
Volume (V1) = (4/3) * π * (0.1 m)^3
Mass (m1) = Density * Volume (V1)
For the second sphere:
Radius (r2) = diameter / 2 = 2 cm / 2 = 1 cm = 0.01 m
Volume (V2) = (4/3) * π * (0.01 m)^3
Mass (m2) = Density * Volume (V2)
Now, we can substitute the values in the gravitational force formula:
F = (G * m1 * m2) / r^2
= (6.674 * 10^-11 N m^2 / kg^2) * (m1) * (m2) / (r^2)
Plug in the values of G, m1, m2, and r, and calculate the gravitational force.