Question

A particle of mass m is released from the top of a hemisphere of radius r. when the particle reached at bottom has speed v. find the normal reaction on the particle by the hemisphere.

Answer 1

Given:

A particle of mass m is released from the top of a hemisphere of radius r. when the particle reached at bottom has speed v.

To find:

Normal reaction on the particle by the sphere at the bottom.

Calculation:

We will apply Conservation of Mechanical Energy to get the kinetic energy at the bottom of the hemisphere.

$\therefore$∆KE = ∆PE

=> ½mv² - 0 = mgr - 0

=> ½mv² = mgr

=> mv²/r = 2mg.

Now, as per Free - Body diagram of block at the bottom of the hemisphere ;

$\therefore \: N = \dfrac{m {v}^{2} }{r}$

$= > \: N = 2mg$

So, final answer is

$\boxed{ \bold{ \large{ \: N = 2mg}}}$

Answer 2

Answer:

N=mg+mv^2/R

Explanation:

Since at the lowest point,centripetal acceleration acts radially outwards the normal reaction would be this.

You can also find value of this by using conservation of energy formula.

P.E=K.E

Since at lowest point P.E=mgR and K.E=1/2mv^2

Find v then substitute in the eqn.

Then value of normal reaction is N=3mg