146560 Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \mathrm{~cm}$ longer than the copper rod at any temperature.
[The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ respectively]

146561 Two metal rods $A$ and $B$ each of length $50 \mathrm{~cm}$ and diameter $4.0 \mathrm{~mm}$ are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ?
[Given linear expansion coefficients of rods $\mathrm{A}$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times$ $\left.10^{-5} /{ }^{\circ} \mathrm{C}\right]$

146562 A circular copper ring at $30^{\circ} \mathrm{C}$ has a hole with an area of $9.98 \mathrm{~cm}^{2}$. It is made to slip onto a steel rod of cross-sectional area of $10 \mathrm{~cm}^{2}$, by raising the temperature of both ring and rod simultaneously by an amount $\Delta \mathrm{T}$. If the coefficient of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $11 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then minimum value of $\Delta \mathbf{T}$ should be

146563 A rod of resistive material of length $L$ is connected to a battery with potential difference $12 \mathrm{~V}$. The resistance per unit length of the rod varies as $\rho(x)=12 x \Omega / m$ where $x$ is the distance from one end of the rod. If the current in the resistive rod transfer energy to thermal energy at the rate of $600 \mathrm{~W}$. Then the length of rod will be

146560 Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \mathrm{~cm}$ longer than the copper rod at any temperature.
[The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ respectively]

146561 Two metal rods $A$ and $B$ each of length $50 \mathrm{~cm}$ and diameter $4.0 \mathrm{~mm}$ are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ?
[Given linear expansion coefficients of rods $\mathrm{A}$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times$ $\left.10^{-5} /{ }^{\circ} \mathrm{C}\right]$

146562 A circular copper ring at $30^{\circ} \mathrm{C}$ has a hole with an area of $9.98 \mathrm{~cm}^{2}$. It is made to slip onto a steel rod of cross-sectional area of $10 \mathrm{~cm}^{2}$, by raising the temperature of both ring and rod simultaneously by an amount $\Delta \mathrm{T}$. If the coefficient of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $11 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then minimum value of $\Delta \mathbf{T}$ should be

146563 A rod of resistive material of length $L$ is connected to a battery with potential difference $12 \mathrm{~V}$. The resistance per unit length of the rod varies as $\rho(x)=12 x \Omega / m$ where $x$ is the distance from one end of the rod. If the current in the resistive rod transfer energy to thermal energy at the rate of $600 \mathrm{~W}$. Then the length of rod will be

146560 Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \mathrm{~cm}$ longer than the copper rod at any temperature.
[The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ respectively]

146561 Two metal rods $A$ and $B$ each of length $50 \mathrm{~cm}$ and diameter $4.0 \mathrm{~mm}$ are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ?
[Given linear expansion coefficients of rods $\mathrm{A}$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times$ $\left.10^{-5} /{ }^{\circ} \mathrm{C}\right]$

146562 A circular copper ring at $30^{\circ} \mathrm{C}$ has a hole with an area of $9.98 \mathrm{~cm}^{2}$. It is made to slip onto a steel rod of cross-sectional area of $10 \mathrm{~cm}^{2}$, by raising the temperature of both ring and rod simultaneously by an amount $\Delta \mathrm{T}$. If the coefficient of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $11 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then minimum value of $\Delta \mathbf{T}$ should be

146563 A rod of resistive material of length $L$ is connected to a battery with potential difference $12 \mathrm{~V}$. The resistance per unit length of the rod varies as $\rho(x)=12 x \Omega / m$ where $x$ is the distance from one end of the rod. If the current in the resistive rod transfer energy to thermal energy at the rate of $600 \mathrm{~W}$. Then the length of rod will be

146560 Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \mathrm{~cm}$ longer than the copper rod at any temperature.
[The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.7 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ respectively]

146561 Two metal rods $A$ and $B$ each of length $50 \mathrm{~cm}$ and diameter $4.0 \mathrm{~mm}$ are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ?
[Given linear expansion coefficients of rods $\mathrm{A}$ and $B$ are respectively, $2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and $1.0 \times$ $\left.10^{-5} /{ }^{\circ} \mathrm{C}\right]$

146562 A circular copper ring at $30^{\circ} \mathrm{C}$ has a hole with an area of $9.98 \mathrm{~cm}^{2}$. It is made to slip onto a steel rod of cross-sectional area of $10 \mathrm{~cm}^{2}$, by raising the temperature of both ring and rod simultaneously by an amount $\Delta \mathrm{T}$. If the coefficient of linear expansion of copper and steel are $17 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $11 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then minimum value of $\Delta \mathbf{T}$ should be

146563 A rod of resistive material of length $L$ is connected to a battery with potential difference $12 \mathrm{~V}$. The resistance per unit length of the rod varies as $\rho(x)=12 x \Omega / m$ where $x$ is the distance from one end of the rod. If the current in the resistive rod transfer energy to thermal energy at the rate of $600 \mathrm{~W}$. Then the length of rod will be