Masses a and b rest on very light pistons that enclose a fluid. there is no friction between the pistons and the cylinders they fit inside. block b has a bigger volume than block a. which of the following is true?

a)density of b is the same as density of a

b)density of b is greater than density of a

c)density of b is smaller than density of a

d)not enough information

D)Not enough information

Explanation:

According to Pascal's principle, the pressure exerted on the two pistons is equal:

Pressure is given by the ratio between force F and area A, so we can write

The force exerted on each piston is just equal to the weight of the corresponding mass: , where m is the mass and g is the gravitational acceleration. So the equation becomes

Now we can rewrite the mass as the product of volume, V, times density, d:

We also know that

So we can further re-arrange the equation (and simplify g as well):

We are also told that block B has bigger volume than block A: . However, this information is not enough to allow us to say if the fraction on the right is greater than 1 or smaller than 1: therefore, we cannot conclude anything about the densities of the two objects.

c. magnitude and direction