A block of mass M is attached to a light string. The string passes over a massless, frictionless pulley and is attached to a solid uniform ball of mass 3M. The ball is at rest and completely submerged in a fluid as shown. What is the ratio of the density of the fluid to the ball?
Fb = (rho)Vg
Fg = mg
The Attempt at a Solution
The forces acting upward must balance the forces acting downward on the ball. Thus,
Fb + Tension = Fg
(rho)Vg + T = 3Mg
We know that the tension in the string is equal to M because it is keeping the block at rest. Thus,
(rho)Vg + Mg = 3Mg
(rho)Vg = 2Mg
Divide both sides by Vg and we obtain:
(rho(fluid)) = 2(rho(ball))
This is not the correct answer. Can someone explain what I'm doing wrong?