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Diya Kibe
Asked: 2022-11-09T17:47:39+05:30 In:

A small disc A slides down with initial velocity equal to zero from the top of a smooth hill of height H having a horizontal portion. What must be the height of the horizontal portion h to ensure the maximum distance s covered by the disc? What is it equal to?
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A small disc A slides down with initial velocity equal to zero from the top of a smooth hill of height H having a horizontal portion. What must be the height of the horizontal portion h to ensure the maximum distance s covered by the disc? What is it equal to?
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  1. Correct Answer – B
    In order to obtain the velocity point (B), we apply the law of conservation of energy.
    So,
    Loss in `PE`=Gain in `KE`
    `m g (H-h) =1/2mv^(2)`
    `:. v=(sqrt[2g(H-h)])`
    Further `h=1/2gt^(2)`
    `:. t=sqrt((2h)/g)`
    Now, `s=v xx t =sqrt[[2g(H-h)]] xx sqrt((2 h//g))`
    or `s=sqrt[[4h(H-h)]]` …..(i)
    For maximum value of s, `(ds)/(dh)=0`
    `:. 1/(2sqrt[[4h(H-h)]]xx4(H))=0` or `h=H/2`
    Substituting `h=H//2` in E.q. `(1)`, we get
    `s=sqrt[[4(h//2)(H-//2)]]=sqrt(H^(2))=H`

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