Question

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?

• A. $g\sqrt{10}$
• B. g
• C. $g\sqrt{2}$
• D. $g\sqrt{6}$

Answer 1

The correct option is A $g\sqrt{10}$

Since the body is given just enough speed to complete the vertical circle

$u^2=5gR$

$v^2=u^2-2gR$

$=5gR-2gR$

$=3gR$

When the velocity is vertical, the body is acted by two acceleration

$a_T{=}^{\prime }{g}^{\prime }$ tangentially and centripetal acceleration

$ac=v^{2}R$ radially.

$ac=v^{2}R=3gRR$

$=3g$

Total acceleration $=\sqrt{a_T^4+a_c^2}$

$=\sqrt{g^2+3g^2}$

$=g\sqrt{10}$