Strain

Q. Figure shows two rods $A$ and $B$ of same length $L$ and same cross-sectional area $S$ but of different material having coefficient of linear expansion ${\alpha }_1$ and ${\alpha }_2$ respectively. They are clamped between two rigid walls, separated by a distance $2L$. This all refers to temp $t^{\circ }\text{C}$. Find the tension in each rod at temp $2t^{\circ }\text{C}$ (Take the young’s modulus for the two rods to be $Y_1$ and $Y_2$ respectively).

1. $\frac{S{Y}_1{Y}_2(2{\alpha }_1+{\alpha }_2)t}{(2Y_1+Y_2)}$
2. $\frac{S{Y}_1{Y}_2({\alpha }_1+2{\alpha }_2)t}{(Y_1+2Y_2)}$
3. $\frac{S{Y}_1{Y}_2({\alpha }_1+{\alpha }_2)t}{(Y_1+Y_2)}$
4. $\frac{S{Y}_1{Y}_2({\alpha }_1+2{\alpha }_2)t}{(Y_1+Y_2)}$

Q. A stone of mass $3\text{kg}$ tied to a light string of length $l=\frac{7}{10}\text{m}$ is whirled in a circular path in a vertical plane. If the ratio of the maximum to minimum tension in the string is $9$, find the speed of the stone at the highest point.

1. $3.5\text{m}$
2. $2.5\text{m}$
3. $7\text{m}$
4. $\frac{2}{7}\text{m}$