A uniform cylindrical rod of length L, cross-section area A and Young's modulus Y is acted upon by the force as shown in Fig. 7(CF).3. The elongation of the rod is

Options

A. `(2FL)/(5AY)`
B. `(3FL)/(5AY)`
C. `(3FL)/(8AY)`
D. `(8FL)/(3AY)`

Answer

D

Explanation

The free body diagram of two parts are shown in Fig. 7(CF).38 (a), (b).

Both the parts of body are stretched by forces shown. Therefore, total elongation is
`Delta l=Delta l_(1)+Delta l_(2)=(3F(2L//3))/(AY)+(2F(L//3))/(AY) =(8FL)/(3 AY)`