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There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be
The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} m ^{2}$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons, the required area of cross section of the rope should be.$.........\times 10^{-4} \,m ^{2}$ (take $g =10\, ms ^{-2}$ )
A uniform cubical block is subjected to volumetric compression, which decreases its each side by $2 \%$. The Bulk strain produced in it is ............
The work done per unit volume to stretch the length of area of cross-section $2 \,mm ^2$ by $2 \%$ will be ....... $MJ / m ^3$ $\left[Y=8 \times 10^{10} \,N / m ^2\right]$
If $\rho $ is the density of the material of a wire and $\sigma $ is breaking stress, the greatest length of the wire that can hang freely without breaking is
A force $F$ is applied on the wire of radius $r$ and length $L$ and change in the length of wire is $l.$ If the same force $F$ is applied on the wire of the same material and radius $2r$ and length $2L,$ Then the change in length of the other wire is
A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal is