A small block with mass m rests on a frictionless horizontal

A small block with mass m rests on a frictionless horizontal tabletop a distance r from a hole in the center of the table (Fig. 5.79). A string tied to the small block passes down through the hole, and a larger block with mass M is suspended from the free end of the string. The small block is set into uniform circular motion with radius r and Speed v. What must v be if the large block is to remain motionless when released?

Solution

We have to apply such a force so that the larger block is still, i.e. the centrifugal force applied by the smaller block due to uniform circular motion should balance the weight of the larger block, i.e.

mv^2/r (centrifugal force) = Mg (weight)

v^2 = rMg/m

v = (Mgr/m)

So the velocity of the uniform circular motion of the small block of mass m should be (Mgr/m)

The answer is velocity =(Mgr/m)