$A$ brass wire $1.8\; m$ long at $27\;^{\circ}C$ is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of $-39\;^{\circ}C$,what is the tension developed in the wire,if its diameter is $2.0\; mm$? (Coefficient of linear expansion of brass $\alpha = 2.0 \times 10^{-5}\; K^{-1}$; Young's modulus of brass $Y = 0.91 \times 10^{11}\; Pa$)

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)

Two wires $A$ and $B$ made of different materials of length $6.0 \ cm$ and $5.4 \ cm$, respectively, and area of cross-sections $3.0 \times 10^{-5} \ m^2$ and $4.5 \times 10^{-5} \ m^2$, respectively, are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is . . . . . . . . . . .

The force constant of a wire does not depend on

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $A$ is the area of cross-section of the wire,the stress in the wire at a height $3L/4$ from its lower end is

$A$ 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: