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A body covered a distance of l metre alo...

A body covered a distance of `l` metre along a semicircular path. Calculate the magnitude of displacement of the body, and the ratio of distance to displacement.

Text Solution

Verified by Experts

If `r` radius of semicircular path, then `l = pi r` or `r = l//pi`.
Magnitude of displacement = diameter `= 2r = (2l)/(pi)`
`:. ("Distance")/("Displacement") = (l)/(2l//pi) = (pi)/(2)`.
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Knowledge Check

  • A body covers a distance of L along a semicircular path. Then the ratio of distance to displacement is

    A
    `(2L)/(pi)`
    B
    `(L )/(pi )`
    C
    `(pi )/(2L)`
    D
    `(pi )/(2)`

  • A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements.

    A
    `(pi)/(2 sqrt(2))`
    B
    `(2 sqrt(2))/(pi)`
    C
    `(pi)/(sqrt(2))`
    D
    `(sqrt(2))/(pi)`

  • A body moves along a curved path of a quarter circle. Calculate the ratio of distance to displacement :

    A
    `11:7`
    B
    `7:11`
    C
    `11: sqrt(2) xx7`
    D
    `7:11 sqrt(2)`