Question

A particle is given an initial speed $u$ inside a smooth spherical shell of radius $R=1m$, such 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. $3g$

Answer 1

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

Since the body is given just enough speed to complete the vertical circle
$u^2=5gR$
$v^2=u^2-2gR$
$v^2=5gR-2gR$ $=3gR$


When the velocity is vertical, the body is acted by two accelerations:
$a_T={}^{\prime }{g}^{\prime }$ tangentially or vertically downwards
and
centripetal acceleration, $a_c=v^2/R$ radially.
$a_c=v^2/R=3g$ $=3g$

Total acceleration:
$=\sqrt{a_T^4+a_c^2}$
$=\sqrt{g^2+(3g{)}^2}$
$=g\sqrt{10}$