A square pland of mass `m_(1)=100kg` and edge length `L=20sqrt2m` is placed on a smooth surface. Two person each mass `m_(2)=m_(3)=50 "kg" ` are at corner of a plank as shown in figure. Two person begin to walk on the plank along two different paths as shown in figure and reach nearest corners. What is magnitude of displacment of plank (in `m`) in the process.

Answer

10

Explanation

Let displacement of plank be represented by `xhati+yhatj`
For x-component
`50[L-x]-100x-50x=0`
`x=(L)/(4)`
Similarly y-component
`50[L-y]-100y-50y=0`
`y=(L)/(4)`
Thus `vecr=-(L)/(4)hati-(L)/(4)hatj` or `|vecr|=(L)/(4)sqrt2`