Question 162: Properties of Matter

Question

Young's moduli of two wires A and B are in the
ratio 7 : 4. Wire A is 2 m long and has radius R.
Wire B is 1.5 m long and has radius 2 mm. If
the two wires stretch by the same length for a
given load, then the value of R is close to :-

Accepted Answer

Given:
$${{{Y_A}} \over {{Y_B}}} = {7 \over 4};\,{L_A} = 2m\,;{A_A} = \pi {R^2}$$
$${F \over A} = Y\left( {{l \over L}} \right);{L_B} = 1.5m\,;{A_B} = \pi {(2mm)^2}$$
given F and $$l$$ are same $$ \Rightarrow $$  $${{AY} \over L}$$ is same
$${{{A_A}{Y_A}} \over {{L_A}}} = {{{A_B}{Y_B}} \over {{L_B}}}$$
$$ \Rightarrow {{\left( {\pi {R^2}} \right)\left( {{7 \over 4}{Y_B}} \right)} \over 2} = {{\pi {{(2\,mm)}^2}.{Y_B}} \over {1.5}}$$
R = 1.74 mm

Answer

1.7 mm

Answer

1.9 mm

Answer

1.3 mm

Answer

1.5 mm

Properties of Matter

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

Choose the correct answer: