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 ......... $J$
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The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied
Rod of constant cross-section moves towards right with constant acceleration. Graph of stress and distance from left end is given as in figure. If density of material of rod at cross section $1$ is $9$ $\frac{{gm}}{{c{m^3}}}$ . Find density at cross section $2$.
An aluminum rod (Young's modulus $ = 7 \times {10^9}\,N/{m^2})$ has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod in order to support a load of ${10^4}$Newton's is
A metal wire having Poisson's ratio $1 / 4$ and Young's modulus $8 \times 10^{10} \,N / m ^2$ is stretched by a force, which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in wire is [in $\left.J / m ^3\right]$
In $CGS$ system, the Young's modulus of a steel wire is $2 \times {10^{12}}$. To double the length of a wire of unit cross-section area, the force required is
The ratio of radii of two wires of same material is $2: 1$. If these wires are stretched by equal force, the ratio of stresses produced in them is $.............$
Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $=2 \times 10^{11}\,Nm ^{-2}$ and $g =10\,ms ^{-2}$ ]
A steel rod of length $\ell$, cross sectional area $A$, young's modulus of elasticity $Y$, and thermal coefficient of linear expansion $'a'$ is heated so that its temperature increases by $t\,^oC$. Work that can be done by rod on heating will be
The work done per unit volume to stretch the length of area of cross-section $2 \,mm ^2$ by $2 \%$ will be ....... $MJ / m ^3$ $\left[Y=8 \times 10^{10} \,N / m ^2\right]$