A light rod of length 2 m is suspended from ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section 0.1 cm sq. and the other of brass of cross-section 0.2 cm sq. Along the rod at what distance a weight may be hung to produce equal stresses in the wires?
`(Y_("Steel") = 2 xx 10^(11) Nm^(-2), Y_("Bass") = 1 xx 10^(11) Nm^(-2))`

Options

A. 4/3 m
B. 2/3 m
C. 1 m
D. 3/2 m

Answer

A

Explanation

Stress `= (T)/(A)rArr(T_(1))/(A_(1))=(T_(2))/(A_(2))rArr (T_(1))/(T_(2))=(1)/(2)`
& for equilibrium
`mg = T_(1)+T_(2)=(3T_(2))/(2)` (After balance)
& `mgx-T_(2)(2)=0` (Target balance)
`-(3T_(2))/(2)x-2T_(2)=0x=(4)/(3)m`