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Figure shows a small block A of mass m k...

Figure shows a small block `A` of mass `m` kept at the left end of `a` plank `B` of mass `M = 2m` and length `l` . The system can side on a horizontal road. The system is started towards right with the initial velocity `v`. The friction coefficient between the road and the plank is `1//2` and that between the plank and the block is `1//4` . Find

(a) the time elapsed before the block separates from the plank
(b) displacement of block and plank relative to ground till that moment.

Text Solution

Verified by Experts

The correct Answer is:
`t=4sqrt((l)/(3g)) (b)S_(A)=4Vsqrt((l)/(3g))-(2)/(3)l,S_(B)=4Vsqrt((l)/(3g))-(5)/(3)l`,

System start moving towards right with velocity `v`.

`=((1)/(2)(3m)g-(1)/(4)mg) /(2m)=(5g)/(8)`
`U_(rel)=0`
`a_(rel)=(5g)/(8)-(g)/(4)=(3g)/(8)`
`:. l=(1)/(2)(3)/(8)g t^(2)`
`t=4sqrt((l)/(3g))`
`S_(1)=vt-(1)/(2)(g)/(4)t^(2)=4vsqrt((l)/(3g))-(2l)/(3)s`
`S_(2)=vt-(1)/(2)(5)/(8)g t^(2)=4vsqrt((l)/(3g))-(5)/(3)l`.
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