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Find alpha, a(Q) and the point of zero a...

Find `alpha, a_(Q)` and the point of zero acceleration when the horizontal force `F` acts on the smooth rod of mass `m` and length `l` which is kept on a horizontal surface.

Text Solution

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`tau_(cm)=I_(cm) alpha`
`F l/4=I(ml^(2))/12 alphaimplies alpha=(3F)/(ml)`
`a_(cm)=F/m`
`a_(Q)=a_(cm)+alpha l/2=Fm+(3F)/(ml) l/2=(5F)/(2m)`
Let acceleration of a point `P` (which is distance `x` between centre of mass) is zero then
`a_(p)=a_(cm)-alphax=0`
`impliesF/m-(3F)/(ml)x=0impliesx=l/3`
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