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Two separate wires $A$ and $B$ are stretched by $2 \,mm$ and $4\, mm$ respectively, when they are subjected to a force of $2\, N$. Assume that both the wires are made up of same material and the radius of wire $B$ is 4 times that of the radius of wire $A$. The length of the wires $A$ and $B$ are in the ratio of $a : b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is
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
A cube of aluminium of sides $0.1\, m$ is subjected to a shearing force of $100\, N$. The top face of the cube is displaced through $0.02 \,cm$ with respect to the bottom face. The shearing strain would be
The elastic potential energy stored in a steel wire of length $20\,m$ stretched through $2 \,m$ is $80\,J$. The cross sectional area of the wire is $.........\,mm ^2$ (Given, $y =2.0 \times 10^{11}\,Nm ^{-2}$ )
A $5\, m$ long aluminium wire ($Y = 7 \times {10^{10}}N/{m^2})$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times {10^{10}}N/{m^2})$ of the same length under the same weight, the diameter should now be, in $mm.$
Two wires $A$ and $B$ of same material have radii in the ratio $2: 1$ and lengths in the ratio $4: 1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......