PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

An aluminium can of cylindrical shape contains 500 cm³ of water. The area of the inner cross section of the can is 125 cm². All measurements refer to 10°C.
Find the rise in the water level if the temperature increases to 80°C. The coefficient of linear expansion of aluminium is 23 × 10^–6 °C^–1 and the average coefficient of the volume expansion of water is 3.2 × 10^–4 °C^–1.

A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm³ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10^–1 °C^–1.

A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm³ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10^–1 °C^–1.

A cube of iron (density = 8000 kg m⁻³, specific heat capacity = 470 J kg⁻¹ K⁻¹) is heated to a high temperature and is placed on a large block of ice at 0°C. The cube melts the ice below it, displaces the water and sinks. In the final equilibrium position, its upper surface just goes inside the ice. Calculate the initial temperature of the cube. Neglect any loss of heat outside the ice and the cube. The density of ice = 900 kg m⁻³ and the latent heat of fusion of ice = 3.36 × 105 J kg⁻¹.

A cube of iron (density = 8000 kg m⁻³, specific heat capacity = 470 J kg⁻¹ K⁻¹) is heated to a high temperature and is placed on a large block of ice at 0°C. The cube melts the ice below it, displaces the water and sinks. In the final equilibrium position, its upper surface just goes inside the ice. Calculate the initial temperature of the cube. Neglect any loss of heat outside the ice and the cube. The density of ice = 900 kg m⁻³ and the latent heat of fusion of ice = 3.36 × 105 J kg⁻¹.

A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will the rod exert on one of the clamps? Area of cross-section of the rod is 2.00 mm². Coefficient of linear expansion of steel is 12.0 × 10^–6 °C^–1 and Young's modulus of steel is 2.00 × 10¹¹ Nm^–2.

A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will the rod exert on one of the clamps? Area of cross-section of the rod is 2.00 mm². Coefficient of linear expansion of steel is 12.0 × 10^–6 °C^–1 and Young's modulus of steel is 2.00 × 10¹¹ Nm^–2.

A ball is dropped on a floor from a height of 2.0 m. After the collision it rises up to a height of 1.5 m. Assume that 40% of the mechanical energy lost goes as thermal energy into the ball. Calculate the rise in the temperature of the ball in the collision. Heat capacity of the ball is 800 J K⁻¹.

A ball is dropped on a floor from a height of 2.0 m. After the collision it rises up to a height of 1.5 m. Assume that 40% of the mechanical energy lost goes as thermal energy into the ball. Calculate the rise in the temperature of the ball in the collision. Heat capacity of the ball is 800 J K⁻¹.

A copper cube of mass 200 g slides down on a rough inclined plane of inclination 37° at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Specific heat capacity of copper = 420 J kg⁻¹ K⁻¹.

A copper cube of mass 200 g slides down on a rough inclined plane of inclination 37° at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Specific heat capacity of copper = 420 J kg⁻¹ K⁻¹.

Two steel rods and an aluminium rod of equal length l₀ and equal cross-section are joined rigidly at their ends, as shown in the figure below. All the rods are in a state of zero tension at 0°C. Find the length of the system when the temperature is raised to θ. Coefficient of linear expansion of aluminium and steel are α_a and α_s, respectively. Young's modulus of aluminium is Y_a and of steel is Y_s. 

Two steel rods and an aluminium rod of equal length l₀ and equal cross-section are joined rigidly at their ends, as shown in the figure below. All the rods are in a state of zero tension at 0°C. Find the length of the system when the temperature is raised to θ. Coefficient of linear expansion of aluminium and steel are α_a and α_s, respectively. Young's modulus of aluminium is Y_a and of steel is Y_s. 

A metal block of density 600 kg m⁻³ and mass 1.2 kg is suspended through a spring of spring constant 200 N m⁻¹. The spring-block system is dipped in water kept in a vessel. The water has a mass of 260 g and the bloc is at a height 40 cm above the bottom of the vessel. If the support of the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is 250 J kg⁻³ K⁻¹ and that of water is 4200 J kg⁻¹ K⁻¹. Heat capacities of the vessel and the spring are negligible.

A metal block of density 600 kg m⁻³ and mass 1.2 kg is suspended through a spring of spring constant 200 N m⁻¹. The spring-block system is dipped in water kept in a vessel. The water has a mass of 260 g and the bloc is at a height 40 cm above the bottom of the vessel. If the support of the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is 250 J kg⁻³ K⁻¹ and that of water is 4200 J kg⁻¹ K⁻¹. Heat capacities of the vessel and the spring are negligible.

A torsional pendulum consists of a solid  disc connected to a thin wire (α = 2.4 × 10^–5°C^–1) at its centre. Find the percentage change in the time period between peak winter (5°C) and peak summer (45°C).
  

A torsional pendulum consists of a solid  disc connected to a thin wire (α = 2.4 × 10^–5°C^–1) at its centre. Find the percentage change in the time period between peak winter (5°C) and peak summer (45°C).
  

A circular disc made of iron is rotated about its axis at a constant velocity ω. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20°C to 50°C, keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2 × 10^–5 °C^–1.

A circular disc made of iron is rotated about its axis at a constant velocity ω. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20°C to 50°C, keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2 × 10^–5 °C^–1.

50 m³ of saturated vapour is cooled down from 30°C to 20°C. Find the mass of the water condensed. The absolute humidity of saturated water vapour is 30 g m⁻³ at 30°C and 16 g m⁻³ at 20°C.