A rock of mass M with a density twice that of water is sitting on the bottom of an aquarium tank filled with water.The normal force exerted on the rock by the bottom of the tank is
A)2Mg
B)Mg
C)Mg/2
D)zero
E)impossible to determine from the information given.

Question

Quizplus · Accepted Answer

The normal force exerted by the bottom of the tank on the rock is equal in magnitude and opposite in direction to the weight of the rock. The weight of the rock is given by W = Mg, where M is the mass of the rock and g is the acceleration due to gravity. Since the density of the rock is twice that of water, its mass per unit volume is twice that of water. This means that for the same volume of water displaced by the rock, the weight of the rock is twice that of the water displaced. However, the buoyant force exerted by the water on the rock is equal to the weight of the water displaced by the rock, which is equal to the weight of the rock. Therefore, the net effect of buoyancy on the rock is zero, and the normal force exerted by the bottom of the tank on the rock is equal to its weight, Mg.

A Rock of Mass M with a Density Twice That