Two wires of same material have lengths in ratio 1 : 2 and their radii are in ratio 1:√ 2 . If the

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8.Mechanical Properties of Solids

medium

Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

$2:\sqrt 2 $

$\sqrt 2 :2$

1:1

1:2

Solution

(c)$l = \frac{{FL}}{{\pi {r^2}Y}}$$ \Rightarrow l \propto \frac{L}{{{r^2}}}$ (F and Y are constant)
$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}}{\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} = \frac{1}{2}{\left( {\sqrt 2 } \right)^2}$
$\frac{{{l_1}}}{{{l_2}}} = 1:1$

Standard 11

Physics

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be

medium

(JEE MAIN-2023)

Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?

easy

One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.

[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\ \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

hard

(JEE MAIN-2024)

Three bars having length $l, 2l$ and $3l$ and area of cross-section $A, 2 A$ and $3 A$ are joined rigidly end to end. Compound rod is subjected to a stretching force $F$. The increase in length of rod is (Young's modulus of material is $Y$ and bars are massless)