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In the given figure all the surfaces are...

In the given figure all the surfaces are smooth. Find the time taken by the block to reach from the free end to the pulley attached to the plank.
Distance between free end and pulley is `l`.

Text Solution

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Equation of motion for M:
`2F=Ma_(2)" " ...(1)`
For m,
`F=m a_(1)" " ...(2)`
Relative acceleration between M and `m=a_(r)=a_(1)+a_(2)`

`a_(1)+a_(2)=(2F)/(M)+(F)/(M)=F[(2)/(M)+(1)/(m)] " " .....(3)`
Let the block m strike the pulley after a time t.
Since,
`l=(1)/(2) a_(r)t^(2)`
`rArr t = sqrt((2l)/(F((2)/(M)+(1)/(M))))`
`rArr t = sqrt((2 Mml)/((2m+M)F))`
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