A uniform plank is resting over a smooth horizontal floor and is pulled by applying a horizontal force at its one end. Which of the following statements are not correct?

Options

A. Stress developed in plank material is maximum at the end at which force is applied and decrease linearly to zero at the other end.
B. A uniform tensile stress is developed in the plank material
C. Since plank is pulled at one end only, plank starts to accelerate along direction of the force. Hence, no stress is developed in the plank material
D. None of these

Answer

BC

Explanation

Deformation force will be same as tension in the rod, which will be there at all points. Hence, (C) is incorrect
Now `m_(1)=(M)/(L)(L-X)`
`m_(2)=(M)/(L)XrArra=(F)/(M)`
and `F'=T =m_(1)a` where F' is the deforming force
`=(M)/(L)(L-X)(F)/(M)=F((L-X))/(L)rArr"stress"=(F')/(A)=(F(L-X))/(AL)`

`rArr` Stress varies linearly with ‘x’. It is maximum at x = 0 and zero at x = L
Hence, (A) is correct