KVPY SA Exam 2015 Question Paper

Question : 17 of 80

Marks: +1, -0

A hollow tilted cylindrical vessel of negligible mass rests on a horizontal plane as shown. The diameter of the base is a and the side of the cylinder makes an angle θ with the horizontal. Water is then slowly poured into the cylinder. The cylinder topples over when the water reaches a certain height h, given by

$h=2a\tanθ$
$h= a\tan^2θ$
$h= a\tan θ$
$h= a/2\tan θ$

Validate

Solution:

(COM at mid pt of filled cylinder)

\sinθ={BC}/{AC};AC={BC}/{\sinθ};AC=h/{\sinθ}

\cosθ={a/2}/{h/{2\sinθ}};

\cosθ= { {a\sinθ}/h};

⇒h = a tan θ

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