Question

. Awagon of m can move without friction along horizontal rails. A simple pendulum consisting of a sphere of mass
mis suspended from the ceiling of the wagon by a string of length I. At the initial moment the wagon and the
pendulum are at rest and the string is deflected through an angle 60° from the vertical. Find the velocity of the
wagon when the pendulum passes through the mean position.​

Answer 1

Answer:

m/M{√[(mgl)/(m+M)]}

Explanation:

If we take the velocity of the wagon as V m/s and the pendulum speed as v m/s. So, we get that when the pendulum is raised by the angle of 60 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.

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)]}.