Question

A simple pendilum is swinging in a vertical plane.The ratio of its potential energies when it is making angles 30°and 60° with the vertical is,

Answer 1

Explanation:

as potential energy= mgl(1-costheta)

so at theta=30

U1=mgl(1-cos30)

=mgl(1-√3/2)

=mgl(2-√3)

2

know at theta=60

U2=mgl(1-cos60)

=mgl(1-1/2)

=mgl(1/2)

= mgl

2

now for ratio

U1/U2. = mgl(2-√3/2). (mgl and 2 will be cancelled)

mgl/2

= 2-√3

1