Two wires ‘A’ and ‘B’ of same material have radii in ratio 2 : 1 and lengths

English

Gujarati

Hindi

8.Mechanical Properties of Solids

medium

Two wires $‘A’$ and $‘B’$ of the same material have radii in the ratio $2 : 1$ and lengths in the ratio $4 : 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

$1:1$

$2:1$

$1:4$

$1:2$

Solution

(a) $F = Y \times A \times \frac{l}{L}$ $⇒$ $F \propto \frac{{{r^2}}}{L}$ $(Y$ and $l$ are constant$)$

$\frac{{{F_1}}}{{{F_2}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}\left( {\frac{{{L_2}}}{{{L_1}}}} \right) = {\left( {\frac{2}{1}} \right)^2}\left( {\frac{1}{4}} \right) = 1$ $⇒$ $\frac{{{F_1}}}{{{F_2}}} = 1:1$

Standard 11

Physics

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

easy

(AIEEE-2005)

$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ……….. $MPa$

hard

In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back. The combined mass of all the persons performing the act, and the tables, plaques etc. Involved is $280\; kg$. The mass of the performer lying on his back at the bottom of the pyramid is $60\; kg$. Each thighbone (femur) of this performer has a length of $50\; cm$ and an effective radius of $2.0\; cm$. Determine the amount by which each thighbone gets compressed under the extra load.

medium

A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be 🙁 $\frac{{mg}}{{AY}}$ is dimensionless)

hard

A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :

hard

Two wires $‘A’$ and $‘B’$ of the same material have radii in the ratio $2 : 1$ and lengths in the ratio $4 : 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

Solution

Similar Questions

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be 🙁 $\frac{{mg}}{{AY}}$ is dimensionless)

Start a Free Trial Now