Question

A small sphere A of radius r rolls without slipping inside a large hemispherical bowl of radius R as shown in figure. If the sphere starts from rest at the top point of the hemisphere find the normal force exerted by the small sphere on the hemisphere when it reaches at the bottom B of the hemisphere :
(1) 17/7mg
(2)2/5mg
(3)5/7mg
(4)7/5mg​

Answer 1

A small sphere A of radius r rolls without slipping inside a large hemispherical bowl of radius R as shown in figure. If the sphere starts from rest at the top point of the hemisphere find the normal force exerted by the small sphere on the hemisphere when it reaches at the bottom B of the hemisphere :

(1) 17/7mg

(2)2/5mg

(3)5/7mg

(4)7/5mg

Velocity on reaching the bottom :

$mg(r - R) = \frac{7}{10} {mv}^{2}$

${v}^{2} = \frac{10}{7} g(r - R)$

$n - mg = \frac{ {mv}^{2} }{r - R}$

$n = \frac{17}{7} mg$

$bts ❤ exo$