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Grade 12th passMechanics

show that the acceleration of a disc rolling down an inclined plane of an angle , theta is 2g sin theta/3, while that of a ball is 5g sin theta /7

Profile image of Dhritimaan Debnath
7 Years agoGrade 12th pass
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1 Answer

Profile image of chirag garg
7 Years ago
 
 acc. parallel to incline of bottom point which is in contact with incline is zero-
 
mgsinθ - f = ma __(1)  ( a= linear acc. parallel to incline)
f×R = I×α __(2)  ( f = frictional force , α= angular acc , I = moment of inertia)
α×R =a __(3)  ( net acc zero)
 
in case of a disc {I = (mR² )/2}, from (1) , (2) and (3),
f = (mgsinθ)/3 and a = (2gsinθ)/3
 
similarly , in case of a ball or solid sphere{I= (2mR²)/5}
f= (2mgsinθ)/7 and a= (5gsinθ)/7
 
 
 
 

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