A force of ${10^3}$ newton stretches the length of a hanging wire by $1$ millimetre. The force required to stretch a wire of same material and length but having four times the diameter by $1$ millimetre is
Medium
Download our app for free and get started
(b) $F = Y \times A \times \frac{l}{L}$ $⇒$ $F \propto {r^2}$ $(Y,l$ and $L$ are constant$)$
If diameter is made four times then force required will be $16$ times. i.e. $16 \times 10^3 N$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A rigid bar of mass $15\,kg$ is supported symmetrically by three wire each of $2 \,m$ long. These at each end are of copper and middle one is of steel. Young's modulus of elasticity for copper and steel are $110 \times 10^9 \,N / m ^2$ and $190 \times 10^9 \,N / m ^2$ respectively. If each wire is to have same tension, ratio of their diameters will be $ ............$
A spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............. $Nm ^{-2}$
A steel rod has a radius $10 \,mm$ and a length of $1.0 \,m$. A force stretches it along its length and produces a strain of $0.32 \%$. Young's modulus of the steel is $2.0 \times 10^{11} \,Nm ^{-2}$. What is the magnitude of the force stretching the rod is ........ $kN$
A uniform metal rod of $2\,\,mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$ . The coefficient of linear expansion of rod is $12\,\,\times\,\,10^{-6}\,/^oC$ . Its Young's modulus of elasticity is $10^{11}\,\,N/m^2$ . The energy stored per unit volume of rod will be ....... $J/m^3$
A rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta°$, the twist angle at the joint will be
A weight of $200 \,kg$ is suspended by vertical wire of length $600.5\, cm$. The area of cross-section of wire is $1\,m{m^2}$. When the load is removed, the wire contracts by $0.5 \,cm$. The Young's modulus of the material of wire will be
A wire of length $50\, cm$ and cross sectional area of $1$ sq. mm is extended by $1\, mm.$ The required work will be $(Y = 2 \times {10^{10}}\,N{m^{ - 2}})$