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  4. A particle is given an initial speed u inside a smooth spherical shell of the radius R=1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-yiopzwrolsiv.png />

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



Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

$u^{2}=5gR$
$\therefore v^{2}=u^{2}-2gR$
$=5gR-2gR=3gR$
Solution

Tangential acceleration at $B$ is
$a_{t}=g$ (downwards)
Centripetal acceleration at $B$ is
$a_{c}=\frac{v^{2}}{R}=3g$
$\therefore $ Total acceleration will be
$a=\sqrt{a_{C}^{2} + a_{t}^{2}}=g \, \sqrt{10}$