What is the force constant k of the spring?

Important Questions on Matter : Structure and Properties

HARD

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A steel wire of length $4.5$ $\mathrm{m}$ and cross-sectional area $3\times {10}^{–5} {\mathrm{m}}^2$ stretches by the same amount as a copper wire of length $3.5$ $\mathrm{m}$ and cross-sectional area of $4\times {10}^{–5} {\mathrm{m}}^2$ under a given load. The ratio of the Young’s modulus of steel to that of copper is:

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A stretching force of $100 \mathrm{kN}$ acts on a steel rod of length $1 \mathrm{m}$ and radius $10 \mathrm{mm}$. The percentage strain produced in the rod is: (${\mathrm{Y}}_{\mathrm{Steel}}=2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$)

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A cube is subjected to a uniform volume compression. If the side of the cube decreases by $1\%$ the bulk strain is

HARD

Physical Science>Physics>Matter : Structure and Properties>Elasticity

The area of cross-section of steel wire is $0.1 {\mathrm{cm}}^2$ and Young’s modulus of steel is $2\times {10}^{11} \mathrm{N}\mathrm{ }{\mathrm{m}}^{–2}$. The force required to stretch the steel wire by$0.1\%$ of it's length is:

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A steel rod of length $1$ $\mathrm{m}$ and radius $10$ $\mathrm{mm}$ is stretched by a force $100$ $\mathrm{k}$$\mathrm{N}$ along its length. The stress produced in the rod is: (${\mathrm{Y}}_{\mathrm{Steel}}$ = $2\times {10}^{11}\mathrm{ }\mathrm{N}\mathrm{ }{\mathrm{m}}^{–2}$ )

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

One end of a nylon rope of length $4.5$ $\mathrm{m}$ and diameter $6$ $\mathrm{mm}$ is fixed to a free limb. A monkey weighing $100$ $\mathrm{N}$ jumps to catch the free end and stays there. The elongation of the rope is: (Given Young’s modulus of nylon = $4.8\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ )

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A copper and a steel wire of same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which causes a total elongation of $1$ $\mathrm{cm}$. The two wires will have:

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

The dimensional formula of Young's modulus is $\left[M^x{L}^{-1}{T}^{-2}\right]$. The value of $x$ is _____.

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A wire stretches by an amount $l$ under a load. If the load and radius both are increased to four times, the stretch caused in the wire is:

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

Two wires of the same length and same material but radii in the ratio of $1:2$ are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

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-section 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 Young’s moduli of the wires respectively, the effective force constant of the system of two wires is

HARD

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A $15$ $\mathrm{kg}$ mass fastened to the end of the steel wire of unstretched length $1.0$ $\mathrm{m}$ is whirled in a vertical circle with an angular velocity of $2$ $\mathrm{rev}$ ${\mathrm{s}}^{–1}$. The cross-section of the wire is $0.05 {\mathrm{cm}}^2$. The elongation of the wire when the mass is at the lowest point of it's path is: (Take $g=10 \mathrm{m}\mathrm{ }{\mathrm{s}}^{–2}$, $Y_{\mathrm{steel}}=2\times {10}^{11} \mathrm{N}\mathrm{ }{\mathrm{m}}^{–2}$ )

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A man grows into a giant such that his linear dimensions increase by a factor of$9$. Assuming that his density remains same, the stress in the leg will change by a factor of:

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A stone of mass $m$ is tied to one end of a wire of length $L$. The diameter of the wire is $D$ and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle $\mathrm{\theta }$ with the vertical. If Young’s modulus of the wire is $Y$, then the increase in the length of the wire is

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

Dimensional formula for Strain is

MEDIUM

Physical Science>Physics>Matter : Structure and Properties>Elasticity

A bar of length $l$, breadth $\mathrm{b}$ and depth $\mathrm{d}$ is supported at its ends and is loaded at the centre by a load $\mathrm{W}$. If $\mathrm{Y}$ is the Young’s modulus of the material of the bar then, the depression $\mathrm{\delta }$ at the centre is:

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

Dimension of Strain is $M^0{L}^x{T}^0$. The value of $x$ is _____.

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

Dimension of a unit of Strain is $\left[{\mathrm{M}}^{\mathrm{x}}{\mathrm{L}}^{\mathrm{x}}{\mathrm{T}}^{\mathrm{x}}\right]$. The value of $x$ is  _____.

EASY

Physical Science>Physics>Matter : Structure and Properties>Elasticity

The adjacent graph shows the extension $\left(∆\mathcal{l}\right)$ of a wire of length 1m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is ${10}^{-6}\mathrm{ }{\mathrm{m}}^2$ , calculate the Young's modulus of the material of the wire.

HARD

Physical Science>Physics>Matter : Structure and Properties>Elasticity

If the ratio of diameters, lengths and Young’s moduli of steel and brass wires shown in the figure are $p$, $q$ and $r$ respectively then, the corresponding ratio of increase in their lengths would be: