Question

A particle initially at rest starts moving from point a on the surface of a fixed smooth hemisphere

Answer 1

Answer:

Initial height is r(1−cosα)

Final height is r(1−sinβ)

Net vertical displacement is r(1−sinβ)−r(1−cosα)=r(cosα−sinβ)

Apply equation of kinematic

v

2

−u

2

=2as

v

2

=2gr(cosα−sinβ)

Normal reaction,

N=mgsinβ−

r

mv

2

0=mgsinβ−

r

m2gr(cosα−sinβ)

3sinβ=2cosα

Hence, the relation is 3sinβ=2cosα