Q 1 :

Consider a rectangular sheet of solid material of length $l$ = 9 cm and width d = 4 cm. The coefficient of linear expansion is $\alpha =3.1\times {10}^{–5 }{\mathrm{K}}^{–1}$ at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity $C_v=900 \mathrm{J} {\mathrm{kg}}^{–1 }{\mathrm{K}}^{–1}$. If the amount of heat supplied to the material is $8.1\times {10}^{2 }\mathrm{J}$ then change in area of the rectangular sheet is:          [2025]

• $2.0\times {10}^{–6 }{\mathrm{m}}^2$

   

• $3.0\times {10}^{–7 }{\mathrm{m}}^2$

   

• $6.0\times {10}^{–7 }{\mathrm{m}}^2$

   

• $4.0\times {10}^{–7 }{\mathrm{m}}^2$

   

Q 2 :

A hole is drilled in a metal sheet. At $27°\text{C}$, the diameter of the hole is 5 cm. When the sheet is heated to $177°\text{C}$, the change in the diameter of the hole is $d\times {10}^{-3}\text{\hspace{0.05em}cm}$. The value of $d$ will be _______ if the coefficient of linear expansion of the metal is $1.6\times {10}^{-5}/°\text{C}$.                      [2023]

Q 3 :

A thin rod having a length of 1 m and area of cross-section $3\times {10}^{-6}{\text{\hspace{0.05em}m}}^2$ is suspended vertically from one end. The rod is cooled from $210°\text{C}$ to $160°\text{C}$. After cooling, a mass M is attached at the lower end of the rod such that the length of the rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are $2\times {10}^{11}{\text{\hspace{0.05em}Nm}}^{-2}$ and $2\times {10}^{-5}{\text{\hspace{0.05em}K}}^{-1}$, respectively. The value of M is ______ kg.  (Take $g=10{\text{\hspace{0.05em}ms}}^{-2}$)                   [2023]