Question

A particle placed at the top of fixed smooth sphere of radius R is gently disturbed. It leaves the contact

with sphere when theta = cos minus ¹ (1/n)


Value of n is​

Answer 1

Keeping in mind that, when it leaves the contact the particle is no more under the influence of the Normal force. Using the conservation of energy till the last point of contact (ie. θ) we get:

K/f

−K/i

=U /i

−U /f

2/1

mv² −0=mgr(1−cosθ)....(1)

where r is the radius of the sphere and m is the mass of the particle. Now using the force balance equation at the point when the particle has acquired this velocity v and lose its point of contact;

mgcosθ= rmv²

..... (2)

Using both equations (1) and (2), we finally get:

cosθ=2−2cosθ

⇒θ=cos −1 ( 3/2 )

Hope it helps you...

Answer 2

Answer:

Hello how are you....you have already got the correct answer