Question

Speed of a transverse wave on a straight wire (mass $6.0 \mathrm{g},$ length $60 \mathrm{c}\mathrm{m}$ and area of cross-section $1.0 \mathrm{m}{\mathrm{m}}^2$  is $90 {\mathrm{m} \mathrm{s}}^{-1}$. If the Young's modulus of wire is $16\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$, the extension of wire over its natural length is:

JEE Main 2020 (07 Jan Shift 1)

Options

• A: $0.03 \mathrm{m}\mathrm{m}$
• B: $0.02 \mathrm{m}\mathrm{m}$
• C: $0.04 \mathrm{m}\mathrm{m}$
• D: $0.01 \mathrm{m}\mathrm{m}$

Question

The area of cross section of the rope used to lift a load by a crane is $2.5\times {10}^{-4}{ \mathrm{m}}^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be
(take $\mathrm{g}=10{ \mathrm{ms}}^{-2}$)

JEE Main 2022 (26 Jul Shift 2)

Options

• A: $6.25\times {10}^{-4}{ \mathrm{m}}^2$
• B: $10\times {10}^{-4}{ \mathrm{m}}^2$
• C: $1\times {10}^{-4}{ \mathrm{m}}^2$
• D: $1.67\times {10}^{-4}{ \mathrm{m}}^2$

Question

A steel wire of length $3.2 \mathrm{m}\left(Y_S=2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{m} \left(Y_{\mathit{C}}=1.1\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}\right)$ , both of radius $1.4 \mathrm{mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{mm}$. The load applied, in Newton, will be: (Given $\pi =\frac{22}{7}$)

JEE Main 2022 (27 Jul Shift 2)

Options

• A: $360$
• B: $180$
• C: $1080$
• D: $154$

Question

A wire of length $L$ is hanging from a fixed support. The length changes to $L_1$ and $L_2$ when masses $1 \mathrm{kg}$ and $2 \mathrm{kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

JEE Main 2022 (29 Jun Shift 1)

Options

• A: $\sqrt{L_1{ L}_2}$
• B: $\frac{L_1+L_2}{2}$
• C: $2L_1-L_2$
• D: $3L_1-L_2$

Question

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times {10}^{-4}$ is _____  $\mathrm{kJ} {\mathrm{m}}^{-3}$. Assume that material is elastic upto the linear strain of $5\times {10}^{-4}$,

JEE Main 2022 (26 Jun Shift 1)

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Question

A square aluminium (shear modulus is $25\times {10}^9{\mathrm{Nm}}^{-2}$) slab of side $60 \mathrm{cm}$ and thickness $15 \mathrm{cm}$ is subjected to a shearing force (on its narrow face) of $18.0\times {10}^4 \mathrm{N}$. The lower edge is riveted to the floor. The displacement of the upper edge is _____ $\mu \mathrm{m}$.

JEE Main 2022 (27 Jul Shift 1)

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Question

In an experiment to determine the Young's modulus, steel wires of five different lengths ($1,2,3,4$ and $5$) but of same cross-section $\left(2{ \mathrm{mm}}^2\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $\mathrm{x}\times {10}^{11}\mathrm{N} {\mathrm{m}}^{-2}$, then the value of $x$ is _____ .

JEE Main 2022 (27 Jul Shift 2)

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Question

Under isothermal condition, the pressure of a gas is given by $P=a{V}^{–3},$ where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to

JEE Main 2023 (13 Apr Shift 1)

Options

• A: $3P$
• B: $P$
• C: $2P$
• D: $\frac{P}{2}$

Question

Two wires each of radius $0.2 \mathrm{cm}$ and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______${10}^{–6} \mathrm{m}$. [Young's modulus for steel $=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{–2}$ and $g=10 \mathrm{m} {\mathrm{s}}^{–2}$]

JEE Main 2023 (10 Apr Shift 1)

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Question

Match List-I with List-II : $\begin{array}{|c|c|c|c|} \hline & \text { List-I } & & \text { List-II } \\ \hline \text { (A) } & \text { A force that restores an elastic body of unit area to its original state } & \text { (I) } & \text { Bulk modulus } \\ \hline \text { (B) } & \text { Two equal and opposite forces parallel to opposite faces } & \text { (II) } & \text { Young's modulus } \\ \hline \text { (C) } & \begin{array}{l} \text { Forces perpendicular everywhere to the surface per unit area } \\ \text { same everywhere } \end{array} & \text { (III) } & \text { Stress } \\ \hline \text { (D) } & \text { Two equal and opposite forces perpendicular to opposite faces } & \text { (IV) } & \text { Shear modulus } \\ \hline \end{array}$ Choose the correct answer from the options given below :

JEE Main 2024 (05 Apr Shift 2)

Options

• A: (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
• B: (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
• C: (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
• D: (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Question

Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4: 1$ and force $F_1$ is applied to $P$, an extension of $∆l$ is produced. The force which is required to produce same extension in $\mathrm{Q}$ is $F_2$. The value of $\frac{F_1}{ F_2}$ is ______.

JEE Main 2024 (29 Jan Shift 2)

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Question

If average depth of an ocean is $4000 \mathrm{m}$ and the bulk modulus of water is $2\times {10}^9 \mathrm{N} {\mathrm{m}}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times {10}^{-2}$. The value of $\alpha$ is _______, (Given, $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}, \rho =1000 \mathrm{kg} {\mathrm{m}}^{-3}$)

JEE Main 2024 (27 Jan Shift 1)

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Question

Each of three blocks $P, Q$ and $R$ shown in figure has a mass of $3 \mathrm{kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005 {\mathrm{cm}}^2$ and Young's modulus $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is _____ $\times {10}^{-4}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

JEE Main 2024 (30 Jan Shift 1)

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Question

Two blocks of mass $2 \mathrm{kg}$ and $4 \mathrm{kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0\times {10}^{-5} \mathrm{m}$ and Young's modulus of the metal is $2.0\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi }$. The value of $\alpha$ is _____. [Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

JEE Main 2024 (31 Jan Shift 2)

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