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A ladder AP of length 5m inclined to a v...

A ladder AP of length `5m` inclined to a vertical wall is slipping over a horizontal surface with velocity of `2m//s`, when A is at distance `3m` from ground. What is the velocity of COM at this moment?

Text Solution

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The correct Answer is:
A, B
`y=sqrt(L^2-x^2)implies(dy)/(dt)=-(x)/(sqrt(L^2-x^2))(dx)/(dt)`

`=-(3xx2)/(4)=-3/2m//s`
`V_(CM)=sqrt(((1dx)/(2dt))^2+(1/2(dy)/(dt))^2)`
`=sqrt((1)^2+(3/4)^2)=1.25m//s`
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Knowledge Check

  • The end A of a ladder AP of length 5m, kept inclined to a vertical wall is slipping over a horizontal surface with velocity of 2m//s , when A is at a distance of 3m from the wall. Velocity of C.M. at this moment is

    A
    `1.25 m//s`
    B
    `0 m//s`
    C
    `1 m//s`
    D
    `2 m//s`

  • A disc of mass 2 kg is rolling on a horizontal surface without slipping with a velocity of 0.1 m/s. What is its rotational kinetic energy?

    A
    `5xx10^(-3)J`
    B
    `2.5xx10^(-3)J`
    C
    `15xx10^(-3)J`
    D
    `8xx10^(-3)J`

  • Rain is falling vertically downward with velocity 4m//s. A man is moving horizontally with velocity 3 m//s , the velocity of rain with respect to man is

    A
    `5m//s` at an angle `tan^(-1)(4//3)` with horizontal
    B
    `5 m//s` at an angle `tan^(-1)(3//4)` with vertical
    C
    `5m//s` at an angle `tan^(-1)(4//3)` with vertical
    D
    Both `(1)` and `(2)`

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