Aparticle of mass 1 g executes an oscillatory motion on the concave surface of a spherical dish of radius 2m placed on a horizontal plane, Figure . If the motion of the particle begins from a point on the dis at a height of 1 cm. from the horizontal plane and coefficient of friction is 0.01 , fing the total distance covered by the particle before coming to rest.

Explanation

Here , ` m = 1 g , R' = 2 m , h = 1 cm `
` mu = 0 . 01 `
potential energy of particle m g h
If d is the distance moved by the particle before coming to rest , then work done against friction is
`W = (mu R) xx d = mu mg xx d`
As P .E . is spent in doing this work
` :. mu mg xx d = m m g h`
`d = (h)/(mu) = (1)/(0.01) = 100 cm = 1 m ` .