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
Medium
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
- 1A $2 \,m$ long rod of radius $1 \,cm$ which is fixed from one end is given a twist of $0.8$ radians. The shear strain developed will beView Solution
- 2If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths isView Solution
- 3$Assertion :$ Stress is the internal force per unitarea of a body.View Solution
$Reason :$ Rubber is more elastic than steel. - 4A pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$ , then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$View Solution
- 5A wire of length $2\, m$ is made from $10\;c{m^3}$ of copper. A force $F$ is applied so that its length increases by $2\, mm.$ Another wire of length 8 m is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by......... $cm$View Solution
- 6The relationship between Young's modulus $Y,$ Bulk modulus $K$ and modulus of rigidity $\eta $ isView Solution
- 7A wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$, the increase in its length is $l$. If another wire of same material but of length $2L$ and radius $2r$ is stretched with a force of $2F$, the increase in its length will beView Solution
- 8A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$View Solution
- 9The elongation of a wire on the surface of the earth is $10^{-4} \; m$. The same wire of same dimensions is elongated by $6 \times 10^{-5} \; m$ on another planet. The acceleration due to gravity on the planet will be $\dots \; ms ^{-2}$. (Take acceleration due to gravity on the surface of earth $=10 \; m / s ^{-2}$ )View Solution
- 10View SolutionDue to addition of impurities, the modulus of elasticity