A SMOOTH SPHERE OF RADIUS R IS MADE TO TRANSLATE IN A STRAIGHT LINE WITH A CONSTANT ACC OF a. A PARTICLE IS KEP ON THE TOP PF THE SPHERE AND IS RELEASED . FIND THE SPEED OF THE PARTICLE WITH RESPECT TO THE ANGE @ IT SLIDES

I HV DEMONSRATED 2 TYPES OF WORKINGS PLS VERIFY IT

IN THE FIRST SCENARIO

THE WORKINGS R FROM AN INERTIAL FRAME OF REFERENCE

SO NO PSUEDO FORCE AND CENTRIFUGAL FORCE IS ACTING ON THE BLOCK

THEREFORE

MV^2/RCOS@=MG

AND

MV^2/RSIN@=MA   ( I AM NOT SURE ABT THIS EQUATION SINCE CENTRIPITAL FORC EIS THE RESULTANT OF ALL THE  FORCES ACTING ON THE SYSTEM)

NOW  FOR THE WORKINGS  FROM THE FRAME OF THE SOHERE

SINCE IT IS AN NON  -INERTIAL FRAME OF REFERENCE PSUEDO FORCE AND CENTRIFUGAL FORCE WILL BE ACTING ON THE SYSTEM

ACC IN THE Y AXIS IS MG-MV^2/R

MV^2R SIN@=MA (APPLYING PSUEDO FORCE)

PLS SOLVE THIS EPIC QUESTION AND HIGHLIGHT MY ERRORS

lets first do it by a simple and short method...

by energy method...

lets work in frame of reference of sphere..

let P be the point where it makes an angle @ with the verticle...

forces acting on particle : pseudo force(=ma); weight(=mg) and normal reaction(=N) 

now, K.E at P = W_{pseudo force} + W_mg + W_N

1/2mv² = maRsin@ + mgR(1-Rcos@) + 0

solve to get v = [2R(asin@ + g -gcos@)]^1/2