The density and breaking stress of a wire are $6 \times 10^4 \ kg/m^3$ and $1.2 \times 10^8 \ N/m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the value on the surface of Earth. The maximum length of the wire without breaking is ............ $m$ (take $g = 10 \ m/s^2$ on Earth).

$A$ body of mass $10 \, kg$ is attached to the end of a wire of length $0.3 \, m$. If the breaking stress of the wire is $4.8 \times 10^7 \, N/m^2$ and its cross-sectional area is $10^{-6} \, m^2$,what is the maximum angular velocity in $rad/sec$ with which it can be rotated in a horizontal plane without breaking the wire?

Which of the following statements is incorrect?

Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.

$A$ spring is stretched by applying a load to its free end. The strain produced in the spring is

$A$ string of cross-sectional area $4 \times 10^{-6} \, m^{2}$ and length $0.5 \, m$ is connected to a rigid body of mass $2 \, kg$. The body is rotated in a vertical circular path of radius $0.5 \, m$. The body acquires a speed of $5 \, m/s$ at the bottom of the circular path. The strain produced in the string when the body is at the bottom of the circle is $\dots \times 10^{-5}$. (Use Young's modulus $Y = 10^{11} \, N/m^{2}$ and $g = 10 \, m/s^{2}$)