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Question Number 18549 by Tinkutara last updated on 24/Jul/17

A particle of mass 1 gram executes an  oscillatory motion on the concave  surface of a spherical dish of radius 2 m,  placed on a horizontal plane. If the  motion of the particle starts from a  point on the dish at the height of 1 cm  from the horizontal plane and the  coefficient of friction is 0.01, how much  total distance will be moved by the  particle before it comes to rest?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{gram}\:\mathrm{executes}\:\mathrm{an} \\ $$$$\mathrm{oscillatory}\:\mathrm{motion}\:\mathrm{on}\:\mathrm{the}\:\mathrm{concave} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{dish}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{2}\:\mathrm{m}, \\ $$$$\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{plane}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{dish}\:\mathrm{at}\:\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{1}\:\mathrm{cm} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{is}\:\mathrm{0}.\mathrm{01},\:\mathrm{how}\:\mathrm{much} \\ $$$$\mathrm{total}\:\mathrm{distance}\:\mathrm{will}\:\mathrm{be}\:\mathrm{moved}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{before}\:\mathrm{it}\:\mathrm{comes}\:\mathrm{to}\:\mathrm{rest}? \\ $$

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