A rolling body of mass $m = 4 k g$ , radius $R$ and radius of gyration $k = R / \sqrt{3}$ is placed as a plank which moves with an acceleration $a_{0} = 1$ ${m s}^{- 2}$ . Find the frictional force acting on the body if it rolls without sliding(in $N$ ).

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Solution

let the friction force be f
now $f = m a_{c m}$ .....(1)
$f R = m R^{2} α / 3$ ...(2)
for no slipping $a_{c m} + α R = 1$ ....(3)
on solving above equation we get
$f = 4 - 3 f \Rightarrow f = 1 N$

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A rolling body of mass m=4kg, radius R and radius of gyration k=R/√3 is placed as a plank which moves with an acceleration a0=1 ms−2. Find the frictional force acting on the body if it rolls without sliding(in N).

let the friction force be fnow f=macm.....(1)fR=mR2α/3...(2)for no slipping acm+αR=1....(3)on solving above equation we getf=4−3f⇒f=1N

A rolling body of mass $m = 4 k g$ , radius $R$ and radius of gyration $k = R / \sqrt{3}$ is placed as a plank which moves with an acceleration $a_{0} = 1$ ${m s}^{- 2}$ . Find the frictional force acting on the body if it rolls without sliding(in $N$ ).

let the friction force be f
now $f = m a_{c m}$ .....(1)
$f R = m R^{2} α / 3$ ...(2)
for no slipping $a_{c m} + α R = 1$ ....(3)
on solving above equation we get
$f = 4 - 3 f \Rightarrow f = 1 N$