The length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.

The mean distance between the atoms of iron is $3 \times 10^{-10} \ m$ and the interatomic force constant for iron is $7 \ N/m$. The Young's modulus of elasticity for iron is:

Two wires of same length having radius of $2 \ mm$ and $1.5 \ mm$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

$A$ wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$,its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant,the increase in length will become.

$A$ metal bar of length $L$ and area of cross-section $A$ is clamped between two rigid supports. For the material of the rod,its Young's modulus is $Y$ and coefficient of linear expansion is $\alpha$. If the temperature of the rod is increased by $\Delta t ^\circ C$,the force exerted by the rod on the supports is

$A$ sphere of mass $2 \,kg$ and diameter $4.5 \,cm$ is attached to the lower end of a steel wire of $2 \,m$ length and area of cross-section $0.24 \times 10^{-6} \,m^2$. The wire is suspended from a $205 \,cm$ high ceiling of a room. When the system is made to oscillate as a simple pendulum, the sphere just grazes the floor at its lowest position. Find the velocity of the sphere at the lowest position. (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)