Question

A small mass is released from rest from the edge of a frictionless, hemispherical bowl. As the mass passes through the bottom of the bowl its acceleration vector is:

Answer 1

Answer:

$a=2g$

Explanation:

Let the radius of the hemisphere is R. The mass is released from rest so the initial speed is equal to zero and acceleration is equal to the g.

By the Newton's 3rd equation,

$v^2=u^2+2as\\v^2=2gR\\v=\sqrt{2gR}$

Now, at the bottom hemisphere the centripetal acceleration will act on the mass and the direction of this force is towards center,

$a_c=\frac{v^2}{R}\\a_c=\frac{(\sqrt{2gR} )^2}{R}\\a_c=2g$

Hence, the acceleration on the bottom of the hemisphere is equal to the 2g.