Q: A simple pendulum is swinging in vertical plane. The ratio of its potential energy when it is making 45° and 90° with the vertical is
(a) 1:1
(b) 1:(√2+1)
(c) √2 ∶ 1
(d) (√2-1) ∶ √2
Ans: (d)
Sol:
P.E when making 45° with vertical
P.E1 = m g l(1-cos45) …(i)
P.E when making 90° with vertical
P.E2 = m g l …(ii)
$ \displaystyle \frac{P.E_1}{P.E_2} = 1 – cos45 $
$ \displaystyle \frac{P.E_1}{P.E_2} = 1 – \frac{1}{\sqrt{2}} $
$ \displaystyle \frac{P.E_1}{P.E_2} = \frac{\sqrt{2}-1}{\sqrt{2}} $