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Question

In figure a solid ball rolls smoothly from rest (starting at height H=10.0 m) until it leaves the horizontal section at the end of the track, at height h=3.0 m. The ball hits the ground at distance x m horizontally from point A. Find the approximate value of x (Give integer value).
[ Take g=10 m/s2]


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Solution


On applying "Law of conservation of mechanical energy" between points B and C.

mgH=12mv2+12Iω2+mgh (taking ground level as reference)

mgH=12mv2+12×25mr2×v2r2+mgh

gH=710v2+gh

Substituting the given values we get,

10×10=710v2+10×3

v2=7007v=10 m/s ........(1)

Motion along y-direction,

h=0×t12×gt2

Substituting the given data we get,

3=12×10×t2t=6100.8 sec .........(2)

Motion along x-direction,

d=vtd=10×0.8=8 m [from (1) and (2)]

Accepted answer : 8

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