A load W produces an extension of 1mm in a thread of radius r. Now if load is made 4W and radius is

English

Gujarati

Hindi

8.Mechanical Properties of Solids

medium

A load $W$ produces an extension of $1mm$ in a thread of radius $r.$ Now if the load is made $4W$ and radius is made $2r$ all other things remaining same, the extension will become..... $mm$

A

$4$

B

$16$

C

$1$

D

$0.25$

Solution

(c) $l = \frac{{FL}}{{AY}}\therefore l \propto \frac{F}{{{r^2}}}$

$\frac{{{l_1}}}{{{l_2}}} = \frac{{{F_2}}}{{{F_1}}}{\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = (4) \times {\left( {\frac{1}{2}} \right)^2} = 1$

${l_2} = {l_1} = 1mm$

Standard 11

Physics

Share

Similar Questions

The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times {10^{10}}\,N/{m^2}$. The force required to stretch by $0.1\%$ of its length is

medium

When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be …….. $cm$

medium

In an experiment, brass and steel wires of length $1\,m$ each with areas of cross section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of $0.2\,mm$ is [Given, the Young’s Modulus for steel and brass are respectively $120\times 10^9\,N/m^2$ and $60\times 10^9\,N/m^2$ ]

hard

(JEE MAIN-2019)

$A$ 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