Two wires $A$ and $B$ made of the same material and areas of cross-section in the ratio $1: 2$ are stretched by the same force. If the masses of the wires $A$ and $B$ are in the ratio $2: 3$,then the ratio of the elongations of the wires $A$ and $B$ is

The Young's modulus of a wire of length $L$ and radius $r$ is $Y \ N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will be

$A$ beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm^2$ is $2 \times 10^{11}\,N/m^2$. The wire is suspended from its support on a given planet. $A$ block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the Earth. The elongation of the wire is (Take $g$ on the Earth $= 10\,m/s^2$):

When a certain weight is suspended from a long uniform wire,its length increases by $1 \ cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one,then the increase in length will be ........ $cm$.

$A$ wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,it is heated so that its temperature rises by $\Delta T$ and it just slips over the wheel. As it cools down to the surrounding temperature,it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$,and its Young's modulus is $Y$,the force that one part of the wheel applies on the other part is: