KVPY SX SB Exam 2018 Question Paper

Question : 94 of 120

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A wheel of radius R is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed u from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is

$u^2 /{2g}$
$u^2 /{2g}+{gR^2}/{2u^2 }$
$u^2/ {4g}$
$R+u^2/ {4g}$

Validate

Solution:

H={u^2\sin^2θ}/{2g}-R\cosθ

{dH}/{dθ}={u^2\sin θ\cosθ}/{ g}-R\sinθ

{dH}/{dθ}=0

\cosθ={-gR}/u^2

H=u^2/{2g}[1-{g^2R^2}/u^4]+{gR^2}/u^2

H=u^2/{2g} -{g R^2}/{2u^2}+{gR^2}/u^2

H=u^2/{2g} +{g R^2}/{2u^2}

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