A boy’s catapult is made of rubber cord which is $42\, cm$ long, with $6\, mm$ diameter of cross -section and of negligible mass. The boy keeps a stone weighing $0.02\, kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released, the stone flies off with a velocity of $20\, ms^{-1}$. Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be

A string of area of cross-section $4\,mm ^{2}$ and length $0.5$ is connected with 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. Strain produced in the string when the body is at the bottom of the circle is $\ldots . . \times 10^{-5}$. (Use Young's modulus $10^{11}\,N / m ^{2}$ and $g =10\,m / s ^{2}$ )

What is Young’s modulus ? Explain. and Give its unit and dimensional formula.

A fixed volume of iron is drawn into a wire of length $L.$ The extension $x$ produced in this wire by a constant force $F$ is proportional to

The force required to stretch a steel wire of $1\,c{m^2}$ cross-section to $1.1$ times its length would be $(Y = 2 \times {10^{11}}\,N{m^{ - 2}})$