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A plank of mass m is placed on a smooth ...

A plank of mass `m` is placed on a smooth surface. Now, a uniform solid sphere of equal mass `m` and radius `R` is placed on the plank as shown in the figure. A force `F` is applied at topmost point of the sphere at an angle of `45^(@)` to the horizontal. Surface between the plank and the sphere is extremely rough so that there is no slip between the plank and the sphere. The force of firction acting between the plank and the sphere is `(F)/(ksqrt(2))`. Find the value of `k`.

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