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Consider a disc of mass m and radius R placed on a rough plank of mass M which in turn is placed on a smooth horizontal surface.Now plank is pulled by a force F and disc starts to roll on the plank. if there is no friction anywhere then, find friction force acting on the body (acting on disc)

Consider a disc of mass m and radius R placed on a rough plank of mass M which in turn is placed on a smooth horizontal surface.Now plank is pulled by a force F and disc starts to roll on the plank.

if there is no friction anywhere then, find friction force acting on the body
(acting on disc)

Grade:12

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
657-2349_Annotation 2020-08-26 204710.png f=ma`……..`(i)`
For plank
`F-f=Ma_(1)`……….`(ii)`
Applying torque equation on disc about centre of mass
`tau=l alpha`
`impliesfR=(mR^(2))/(2)alpha`........`(iii)`
For pure rolling
`a_(1)=a+Ralpha`.......`(iv)`
Solving the four equations, we get
`f=(Fm)/(m+3M)`, `alpha=(2F)/((m+3M)R)`

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