Saved Bookmarks
| 1. |
A pendulum consisting of a small sphere of mass m suspended by aninextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 mg, then the maximum angular amplitude of the displacement from the vertical can be |
|
Answer» `0^(@)` length of pendulum = l Let at any instant the amplitude = `THETA` Then ACCORDING to CONSERVATION of energy K.E. = P.E. `(1)/(2)mv^(2)=mg(l-lcostheta)` `mv^(2)=2mgl(1-costheta)` Equation of motion is `T-mg=(mv^(2))/(l)` or `T=mg+(mv^(2))/(l)` `T=mg+2mg(1-costheta)` or `2mg=mg+2mg-2mgcostheta` or `2mg costheta=mgorcostheta=(1)/(2)` `therefore theta=60^(@)` |
|