The mass of pendulum bob is m It is left from its horizontal position It collides elastically with - Physics - Moving Charges And Magnetism

Question

The mass of pendulum bob is m It is left from its horizontal
position It collides elastically with another body of mass 2m
situated at its mean position The angle made by the pendulum with
the vertical after rebound will be

Sanjay Singh · Accepted Answer

Dear student
Applying conservation of energy for mass m mgl=12m×v2 (l is the length of the string)v=2glAs collision is elastic so using the formulav1=m1-m2m1+m2(u1)+2m2u2m1+m2=m-2mm+2m(2gl)+2m2(0)m1+m2=-2gl3so pendulum bob  wll start rising again toward the direction from which it cameLet the  pendulum bob rises to a height where string makes an angle of θ with the vertical
Now  applying conservation of energy for mass m of bobEnergy at lowest position=0+12m×v21=mgl(1-cosθ)+0  ( potential energy is chosen to be zero at the lowest position and at highest position of the bob its kinetic energy is zero)12m×(2gl3)2=mgl(1-cosθ)12×(2gl9)=gl(1-cosθ)(19)=(1-cosθ)cosθ=1-19=89θ=cos-1(89)Regards

The mass of pendulum bob is m. It is left from its horizontal position. It collides elastically with another body of mass 2m situated at its mean position. The angle made by the pendulum with the vertical after rebound will be