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A simple pendulum with a bob of mass m s...

A simple pendulum with a bob of mass m swings with an angular amplitude of `40^@`. When its angular displacement is `20^@`, the tension in the string is greater than `mg cos 20^@`

Text Solution

Verified by Experts

As the angular amplitude of the pendulum is `40^@`, the bob will be in the mid of the equilibrium position and the extreme position as shown in the figure

`:.` `T=mgcos20^@+(mv^2)/(l)`
`(mv)^2/l` is always a positive quantity.
Hence, `Tgtmgcos20^@`
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Knowledge Check

  • a simple pendulum with a bob of mass m savings with an angular amplitude of 40^(@) . When its angular displacement is 20^(@) , the tension in the strings is-

    A
    less than mg cos `20^(@)`
    B
    greater than mg cos `20^(@)`
    C
    equal to mg cos `20^(@)`
    D
    unpredictable

  • 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

    A
    `3 sqrt(3) mg`
    B
    `(mg)/(2)(3 sqrt(3)-2)`
    C
    `(1)/(2)mg((3)/(sqrt(3)+2))`
    D
    `(1)/(2)mg(3- sqrt(2))`

  • A simple pendulum of mass 'm' , swings with maximum angular displacement of 60^(@) . When its angular displacement is 30^(@) ,the tension in the string is

    A
    Less than mg `cos 30^(@)`
    B
    Equal to `mg cos 30^(@)`
    C
    Greater than `mg cos (30^(@)`
    D
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