KVPY SB SX Exam 2011 Question Paper

Question : 93 of 120

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Figure below shows a small mass connected to a string, which is attached to a vertical post. If the ball is released when the string is horizontal as shown, the magnitude of the total acceleration (including radial and tangential) of the mass as a function of the angle θ is

$g\sinθ$
$g√{3\cos^2θ+1}$
$g\cos θ$
$g√{3\sin^2θ+1}$

Validate

Solution:

Radical acceleration

=V^2/R={2gl\sinθ}/l=2g\sinθ

tangential acceleration = g cos θ
total acceleration

= √{4g^2\sin^2θ+g^2\cos^2θ}

=g√{1+3\sin^2θ}

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