A light rod AB of length 2 mis suspended from the ceiling horizontally by means of two vertical wires as show in Fig. One of the wires is made of steel of cross-section `0.1 cm^(2)` and the other of brass of crosssection 0. `cm^(2)` . The Young's modulus of brass is `1.0 xx 10^(11)`" Nm and of steel is `2.0 xx 10^(11) Nm^(-2)`. Aweight Wis hung met point Cat a distance x from end A. It is found that the stress in the two wires is the same when `x = (n)/(3)` metre Find the value of n.

Answer

4

Explanation

If `T_(a) ` and `T_(b)` are the tensions in steel and brass wires then the stress in them will be the same if
`(T_(s))/(A_(s)) =(T_(b))/(A_(b)) implies (T_(s))/(A_(b)) = (A_(s))/(A_(b)) = (0.1 cm^(2))/(0.2 cm^(2)) = (1)/(2)`

Since the system is in equilibrium the moments of forces `T_(a) ` and `T_(b)` about C will be equal ie
`T_(s) xx x = T_(b) xx (2-x)`
`implies x =2 (2-x) implies x = (4)/(3) ` metre `( because T_(b) = 2T_(s))`
Thus the value of n =4