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

Question

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

TestHub · Accepted Answer

Speed at lowest point, to just complete the circle,

$u^{2} = 5 g R$

$∴$ Speed, when velocity becomes vertical, is

$v^{2} = u^{2} - 2 g R$

$v^{2} = 5 g R - 2 g R = 3 g R$

Tangential acceleration at $B$ is

$a_{t} = g$ (downwards)

Centripetal acceleration at $B$ is

$a_{c} = \frac{v^{2}}{R} = 3 g$

$∴$ Total acceleration will be,

$a = \sqrt{a_{C}^{2} + a_{t}^{2}} = g \sqrt{10}$

Physics - Circular Motion Question with Solution | TestHub

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