A simple pendulum with a bob of mass 'm' swings with angular amplitude of `60^@`. When its angular displacement is `30^@`, the tension in the strings would be

Options

A. `(1)/(2) mg (3sqrt3-2)N`1
B. `1mg (2sqrt3-2)N`
C. `mg (3sqrt3-2)N`
D. `2mg(3 sqrt3-2)N`

Answer

A

Explanation

`Let theta_(1)=60^(@) and theta_(2)=30^(@)`
According to the law of conservation of energy,
`(1)/(2)mv^(2)=mgl(cos theta_(1)- costheta _(2))`
`implies(mv^(2))/(l)=2mg(cos theta_(1)- cos theta_(2))`
At 'B' tension `T= mg cos theta _(2)+(mv^(2))/(l)`
`mg cos theta _(2)+2mg (cos theta_(2)- cos theta_(1))`
`=mg(3 cos theta_(2)-2 cos theta_(1))`
`=mg((3sqrt3)/(2)-1)`
`=(1)/(2)mg (3sqrt3-2)N`.