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A car is moving in a circular horizonta ...

A car is moving in a circular horizonta track of radius 10m with a constant speed of 10 m/s. A pendulum bob is suspended from the roof of the cat by a light rigid rod of length 1.00m. The angle made by the rod with track is

A

zero

B

`30^(@)`

C

`45^(@)`

D

`60^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
The forces acting on the bob are (i) its weight `mg` and (ii) centripetal force `F_(c)=mv^(2)//r`.Resolving these force into components along and perpendicular to rod (see figure), we have (since the bob is in equilibrium)
`T=mg cos theta+F_(c) sin theta` (1)
and `mg sin theta+F_(c) cos theta` (2)
From Eq.(2) `mg sin theta=(mv^(2))/r cos theta`
`rArr tan theta=v^(2)/(rg)=(10)^(2)/(10xx10)=1`, which gives `theta=45^(@)`.
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Knowledge Check

  • A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the vertical is (g = 10 m//s^(2))

    A
    zero
    B
    `30^(@)`
    C
    `45^(@)`
    D
    `60^(@)`

  • A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10ms^(-1) . A plumb bob is suspended from the roof of the car by a string of length 1m. The angle made by the string with vertical is (g = 10ms^(-2))

    A
    `0^(@)`
    B
    `30^(@)`
    C
    `45^(@)`
    D
    `60^(@)`

  • A bus is moving in a circular horizontal track of radius 10 m with a constant speed 10 m//s . A plumb bob is suspended from the roof of length 1.0m. The angle made by the rod with the track is (take g=10 m//s^2 )

    A
    zero
    B
    `30^@`
    C
    `45^@`
    D
    `60^@`