Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$

Young's modulus of rubber is ${10^4}\,N/{m^2}$ and area of cross-section is $2\,c{m^2}$. If force of $2 \times {10^5}$ dynes is applied along its length, then its initial length $l$ becomes

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2\, m$, then the stress produced in the wire is

A thin $1 \,m$ long rod has a radius of $5\, mm$. A force of $50\,\pi kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01\, mm$, which of the following statements is false ?

A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :

Increase in length of a wire is $1\, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be  ........ $mm$