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A simple pendulum of length L and mass (...

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit `-phi` and `+phi`. For an angular displacement `theta(|theta|ltphi)`, the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions:

A

(a) `Tcos theta=Mg`

B

(b) `T-Mgcostheta=(MV^2)/(L)`

C

(c) The magnitude of the tangential acceleration of the bob `a_T=g sin theta`

D

(d) `T=Mg cos theta`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Since the body is moving in a circular path, it needs centripetal force `(Mv^2//l)`.
`:. T-mgcostheta=MV^2//l`
Also the tangential acceleration acting on the mass is `g sin theta`.
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Knowledge Check

  • A simple pendulum of Length l and mass (M) is oscillating in a plane about a vertical line between the angular limits -phi "to" +phi . For an angular displacement theta ( lt |phi|) , , the tension in the string T and velocity of the bob V are related as-

    A
    `T cos theta = Mg`
    B
    T = Mg cos `theta + MV^(2)//R`
    C
    Tangential acceleration is g sin`theta`
    D
    T =Mg cos `theta`

  • If a simple pendulum of length l has maximum angular displacement theta , then the maximum velocity of the bob is

    A
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    B
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    D
    `sqrt(2g l)`

  • A simple pendulum of length l and mass (bob) m is suspended vertically. The string makes an angle theta with the vertical. The restoring force acting on the pendulum is

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    `mg tan theta`
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