A wire extends by 1 mm when a force is applied. Double force is applied to another wire of same mate

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8.Mechanical Properties of Solids

medium

A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........

$8$

$4$

$2$

$1$

Solution

(a)$l = \frac{{FL}}{{\pi {r^2}r}}$==> $l \propto \frac{F}{{{r^2}}}$ (Y and L are constant)
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{F_2}}}{{{F_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = 2 \times {(2)^2} = 8$
${l_2} = 8{l_1} = 8 \times 1 = 8mm$

Standard 11

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(AIEEE-2012)

What is the percentage increase in length of a wire of diameter $2.5 \,mm$, stretched by a force of $100 \,kg$ wt is ……………… $\%$ ( Young's modulus of elasticity of wire $=12.5 \times 10^{11} \,dyne / cm ^2$ )

medium

The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \;kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?

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medium

Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should be

medium

A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........

Solution

Similar Questions

What is the percentage increase in length of a wire of diameter $2.5 \,mm$, stretched by a force of $100 \,kg$ wt is ……………… $\%$ ( Young's modulus of elasticity of wire $=12.5 \times 10^{11} \,dyne / cm ^2$ )

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What should be the shape of the pillars or column in building and bridge ?

Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should be

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