A mass m is hanging on a string that passes over a pulley and is then attached to another mass 3m that is resting on a horizontal table.Neglect friction.Mass m is held motionless and is then released.When it has fallen a distance h,it will have a speed v which can be calculated from the formula
E)None of these is correct.

Question

Quizplus · Accepted Answer

The potential energy of mass m is given by mgh where h is the distance the mass falls. This potential energy is converted into kinetic energy (1/2)mv^2 when the mass reaches the bottom. The tension in the string is the same throughout and is equal to the weight of the mass m, which is mg. The weight of the mass 3m is 3mg. Therefore, the net force acting on the system is (3mg - mg) = 2mg, which causes the mass 3m to accelerate with an acceleration of 2g.

Using the kinematic equation v^2 = u^2 +2as, where u is the initial velocity (which is zero), a is the acceleration (which is 2g), and s is the distance the mass 3m moves (which is h), we get:

v^2 = 0 + 2(2g)h = 4gh
v = sqrt(4gh)

Substituting the given values, we get:

v = sqrt(4gh) = sqrt(4*9.81*h) = 3.13*sqrt(h)

Therefore, the correct answer is B.

A Mass M Is Hanging on a String That Passes