Question #4399

a small block of mass m lies on top of hemisphere of radiys R which is smooth. what minimum horizontal velocity block should be given so that it may not slide down along surface?

Expert's answer

Let t-time of falling

v-speed

g-const

then at any period vt=gt^2 /2

it should be>=R

vt=gt^2 /2*& t=2v/g

vt=v*2v/g=2v^2/g>=R

so ans v>=sqrt(0.5gR)

v-speed

g-const

then at any period vt=gt^2 /2

it should be>=R

vt=gt^2 /2*& t=2v/g

vt=v*2v/g=2v^2/g>=R

so ans v>=sqrt(0.5gR)

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