A particle is projected with a speed `v_(0) = sqrt(gR)`. The coefficient of friction the particle and the hemi- spherical plane is `mu = 0.5` Then , the acceleration of the partical is

Options

A. `g`
B. `(sqrt(5)g)/(2)`
C. `sqrt(2)g`
D. none of these

Answer

B

Explanation

When the particle comes with the contact of hemisphere surface it will slide and friction will be kinetic nature This kinetic friction will provided tangential acceleration to the particle Tangential acceleration of the particle

`a_(1) = (mu mg)/(m) = mu mg = (g)/(2)larr`
Normal acceleration of the particle
`a_(n) = (v^(2))/(R ) = (gR)/(R ) = g uarr`
Net acceleration of the particle
`a_(net) = sqrt(a_(1)^(2) + a_(n)^(2) = sqrt((g^(2))/(4) + g^(2)) = (sqrt(5)g)/(2) `