Particles of m1 and m2 (m2>m1) are connected by a line in extensible string passing over a smooth fixed pulley. Initially, both masses hang vertically with mass m2 at a height x above the floor. If the system is released from rest, with what speed will mass m2 hit the floor and the mass will rise a further distance (m2-m1) x) /m1+m2 after this occurs

The velocity with which the mass will hit the floor is

Explanation:

If the tension in the string is , for we have

,

and for the mass

From these equations we solve for and get:

The kinematic equation

gives the final velocity of a particle, when its initial velocity was , and has traveled a distance while undergoing acceleration .

In our case

(the initial velocity of the particles is zero)

which gives us

which is the velocity with which the mass will hit the floor.