Abody of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius r. prove that the body leaves the sphere when 0 = cos(2/3).

Explanation:

Given that,

Mass = m

Radius = r

Angle

Prove that,

The body leaves the sphere when

When the particle was contact

.....(I)

Using conservation of energy

....(II)

From equation (I) and (II)

The body leaves the sphere when

Hence proved.

= initial pressure

= final pressure = 2

= initial volume

= final volume = /4

= initial temperature = 20 c = 20 + 273 = 293 k

= final temperature = ?

using the equation