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A simple pendulum swings with angular am...

A simple pendulum swings with angular amplitude `theta`. The tension in the string when it is vertical is twice the tension in its extreme position. Then, ` cos theta` is equal to

A

`1//3`

B

`1//2`

C

`2//3`

D

`3//4`\

Text Solution

Verified by Experts

The correct Answer is:
4
`T-mg cos theta=(mv^(2))/R=0`
(v=0 at extreme position)
`T= mg cos theta.....(i)`
At mean position
`2T-mg=mv^(2).....(2)`
alos, `v=sqrt(2g(R-Rcos theta)).....(3)`
from (2) and (3)
`2T-mg =m/R 2gR(1-cos theta)`

`T=3/2 mg -mg cos theta.....(4)`
from (1) and (4)
`2mg cos theta=(3mg).2`
`cos theta=3/4`
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Knowledge Check

  • A simple pendulum oscillates with an anglular amplitude of theta . If the maximum tension in the string is 3 times the minimum tension, then the value of cos theta is

    A
    `(1)/(2)`
    B
    `(2)/(3)`
    C
    `(3)/(4)`
    D
    `(3)/(5)`

  • Tension in the string is minimum when the pendulum is at

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    mean position
    B
    extreme position
    C
    mid way between mean and extreme position
    D
    any position

  • A simple pendulum has a bob of mass m and swings with an angular amplitude phi . The tension in thread is T . At a certain time the string makes an angle theta with the vertical (theta le phi)

    A
    `T =mg cos theta` for all value of `theta`
    B
    `T = mg cos theta` for only `theta = phi`
    C
    `T=mg,"for" theta =cos^(-1)[(1)/(3)(2cos phi+1)]`
    D
    T will be larger for smaller values of `theta`

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