With how much force must you push down on a solid ball of aluminum of radius 9 cm in order for it to be halfway submerged in mercury? (The densities of aluminum and mercury are 2700 kg/m3 and 13,690 kg/m3 respectively.)

Explanation:

According to the Archimedes Principle, the buoyancy force exerted on a body is equal to the displaced weight of fluid, an external force is needed to guarantee the equilibrium of the solid ball, since denstity of aluminium is lower than denstity of mercury. The equation of equilibrium is:

b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.