A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m, that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is _____

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$g \sqrt{10}$

$g \sqrt{2}$

answer is A.

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Detailed Solution

$\begin{array}{l} u^{2} = 5 gR \\ v^{2} = u^{2} - 2 gR \\ = 5 gR - 2 gR = 3 gR \end{array}$
Tangential acceleration at B is at = g (downwards)
Centripetal acceleration at B is
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$a_{c} = \frac{v^{2}}{R} = 3 g$
$∴$ Total acceleration will be
$a = \sqrt{a_{c}^{2} + a_{t}^{2}} = g \sqrt{10}$

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