A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........
Medium
Download our app for free and get started
(a)$l = \frac{{FL}}{{\pi {r^2}r}}$==> $l \propto \frac{F}{{{r^2}}}$ (Y and L are constant)
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{F_2}}}{{{F_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = 2 \times {(2)^2} = 8$
${l_2} = 8{l_1} = 8 \times 1 = 8mm$
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{F_2}}}{{{F_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = 2 \times {(2)^2} = 8$
${l_2} = 8{l_1} = 8 \times 1 = 8mm$
Download our appand 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.*
Similar Questions
- 1If the Young's modulus of the material is $3$ times its modulus of rigidity, then its volume elasticity will beView Solution
- 2A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross section area $S$ and length $L$. $L$ is slighly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel.As it cools down to surronding temperature, it presses the semicircular parts together. If the coefficint of linear expansion of the metal is $\alpha$, and its young's modulus is $Y$, the force that one part of wheel applies on the other part isView Solution
- 3View SolutionYoung’s modulus of perfectly rigid body material is
- 4View SolutionIn which case there is maximum extension in the wire, if same force is applied on each wire
- 5The breaking stress of a wire of length $L$ and radius $r$ is $5$ $kg - wt/{m^2}$. The wire of length $2l$ and radius $2r$ of the same material will have breaking stress in $kg - wt/{m^2}$View Solution
- 6A steel wire having a radius of $2.0\, mm$, carrying a load of $4\, kg$, is hanging from a ceiling. Given that $g = 3.1\pi \,m{s^{ - 2}}$ , what will be the tensile stress that would be developed in the wire?View Solution
- 7A uniform plank of Young’s modulus $Y $ is moved over a smooth horizontal surface by a constant horizontal force $F.$ The area of cross section of the plank is $A.$ The compressive strain on the plank in the direction of the force isView Solution
- 8On all the six surfaces of a unit cube, equal tensile force of $F$ is applied. The increase in length of each side will be ($Y =$ Young's modulus, $\sigma $= Poission's ratio)View Solution
- 9An increases in pressure required to decreases the $200$ litres volume of a liquid by $0.004\%$ in container is .......... $kPa$ (Bulk modulus of the liquid $= 2100\, MPa$)View Solution
- 10The elastic limit of brass is $379\,MPa.$ .......... $mm$ should be the minimum diameter of a brass rod if it is to support a $400\,N$ load without exceeding its elastic limit .View Solution