When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ......... $joule$ $(g = 9.8\,metres/se{c^2})$
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A string of area of cross-section $4\,mm ^{2}$ and length $0.5$ is connected with a rigid body of mass $2\,kg$. The body is rotated in a vertical circular path of radius $0.5\,m$. The body acquires a speed of $5\,m / s$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is $\ldots . . \times 10^{-5}$. (Use Young's modulus $10^{11}\,N / m ^{2}$ and $g =10\,m / s ^{2}$ )
A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$
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
A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\ N$ to the lower end. The weight stretches the wire by $1\ mm$. Then the elastic energy stored in the wire ......... $J$
One end of a uniform rod of mass $m_1$ and crosssectional area $A$ is hung from a ceiling. The other end of the bar is supporting mass $m_2$. The stress at the midpoint is
The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.
Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2\, m$, then the stress produced in the wire is
A steel wire is $1 \,m$ long and $1 \,mm ^2$ in area of cross-section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$ is ........ $N$