Question 425: Properties of Matter

Question

A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm
2
and length $$\sqrt 3 $$ m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30$$^\circ $$ and 60$$^\circ $$, respectively. If elongation in copper wire is ($$\Delta {l_c}$$) and elongation in steel wire is ($$\Delta {l_s}$$), then the ratio $${{\Delta {l_c}} \over {\Delta {l_s}}}$$ is .............. .
[Young's modulus for copper and steel are 1 $$ 	imes $$ 10
11
N/m
2
and 2 $$ 	imes $$ 10
11
N/m
2
respectively.]

Accepted Answer

$${{{T_s}} \over 2} = {T_c}{{\sqrt 3 } \over 2}$$
$${T_s} = \sqrt 3 {T_c}$$
$$\Delta l = {{Tl} \over {Ay}}$$
$$ 	herefore $$ $${{\Delta {l_c}} \over {\Delta {l_s}}} = \left( {{{{T_c}} \over {{T_s}}}} ight)\left( {{{{l_c}} \over {{l_s}}}} ight)\left( {{{{Y_s}} \over {{Y_c}}}} ight)$$
$$ = \left( {{1 \over {\sqrt 3 }}} ight)\left( {{{\sqrt 3 } \over 1}} ight)\left( {{{2 	imes {{10}^{11}}} \over {1 	imes {{10}^{11}}}}} ight) = 2.00$$

Properties of Matter

Integer / Numeric Answer Type