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The ratio of lengths of two rods $A$ and $B$ of same material is $1 : 2$ and the ratio of their radii is $2 : 1$, then the ratio of modulus of rigidity of $A$ and $B$ will be
The work done in increasing the length of a metre long wire of cross-sectional area ........ $J.$ $1\,mm^2$ through $1\,mm$ will be $(Y = 2 \times 10^{11}\,Nm^{-2})$
The work done per unit volume to stretch the length of area of cross-section $2 \,mm ^2$ by $2 \%$ will be ....... $MJ / m ^3$ $\left[Y=8 \times 10^{10} \,N / m ^2\right]$
The temperature of a wire of length $1$ metre and area of cross-section $1\,c{m^2}$ is increased from $0°C$ to $100°C$. If the rod is not allowed to increase in length, the force required will be $(\alpha = {10^{ - 5}}/^\circ C$ and $Y = {10^{11}}\,N/{m^2})$
A bar of cross-sectional area $A$ is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane $BB'$ making an angle $\theta $ with the length The ratio of tensile stress to the shearing stress on the plane $BB'$ is
The bulk modulus of rubber is $9.1\times 10^8\,N/m^2$. To ......... $m$ depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\,\%$ .