Question

a wagon of m can move without friction along horizontal rails a simple pendulum consisting of a sphere of mass M is suspended from the ceiling of the Wagon by a string of length L at the initial moment the WagonR and the pendulum at rest and the string is deflected through an angle 60 degree from the vertical find the velocity of the Wagon when the pendulum passes through the mean position

Answer 1

Answer:

Here is the correct answer

Answer 2

Answer:

m/M{√[(mgl)/(m+M)]}.

Explanation:

From the question we get that the pendulum is raised by the angle of 60 so the length by which it is raised will be l*cos60 = 1/2l or l/2. So, the difference in the height will be l-l/2 = l/2. So, from the conservation of momentum we get that the kinetic energy will be equal to the potential energy where the potential energy is mgl/2 and the kinetic energy is 1/2(m+M)v^2. Taking the velocity of the wagon as V m/s and the pendulum speed as v m/s.

So, mgl/2 = 1/2(m+M)v^2 which on solving we will get that v=√[(mgl)/(m+M)] and the law of conservation of momentum states that mv=MV or the velocity V will be m/M{√[(mgl)/(m+M)]}.