Question 144: Properties of Matter

Question

Two steel wires having same length are
suspended from a ceiling under the same load.
If the ratio of their energy stored per unit
volume is 1 : 4, the ratio of their diameters is:

Accepted Answer

$${{du} \over {dv}}$$ = $${1 \over 2}$$ $$ 	imes $$ stress ÃÂ strain
= $${1 \over 2}{F \over A} 	imes {F \over {AY}}$$ $$ \propto $$ $${1 \over {{A^2}}}$$ $$ \propto $$ $${1 \over {{d^4}}}$$
$${{du} \over {dv}}$$ = $${1 \over 4}$$
$$ \Rightarrow $$ $${\left( {{{{d_1}} \over {{d_2}}}} ight)^4}$$ = 4
$$ \Rightarrow $$ $${{{d_1}} \over {{d_2}}} = {\left( 4 ight)^{{1 \over 4}}}$$ = $$\sqrt 2 :1$$

Answer

1 : 2

Answer

2 : 1

Answer

$$1:\sqrt 2 $$

Answer

$$\sqrt 2 :1$$

Properties of Matter

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

Choose the correct answer: