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 developed in the plank material.
D. none of these

Answer

B, C

Explanation

Since force is applied at one end only, the plank starts to accelerate along the direction of the force and a stress is developed in its material. Hence option c is incorrect.

To calclate stress in the material of the plank , at a distance `d` form the end at which force is applied the free body diagrams are consdered as shown in the figure.
`:.F=m/(l-x)a...........i`
`F-F'=m/lxa`.......ii
From eqn i and ii
`F'=(F(l-x))/l`
`:. Stress=(F')/A=(F(l-x))/(Al)`
where `A` is cross sectional area of the plank.
It shows that stress varies linearly with `x`. It is maximum at `x =0` and zero at `x=l`.