We can solve this problem using the formula for heat transfer through a rod, which is as follows: Q = (kA(T₁ - T₂)) / L where: - Q is the heat transferred, - k is the thermal conductivity, - A is the cross-sectional area, - (T₁ - T₂) is the temperature difference, - L is the length of the rod. SinceRead more
We can solve this problem using the formula for heat transfer through a rod, which is as follows:
Q = (kA(T₁ – T₂)) / L
where:
– Q is the heat transferred,
– k is the thermal conductivity,
– A is the cross-sectional area,
– (T₁ – T₂) is the temperature difference,
– L is the length of the rod.
Since the rods are connected end to end, heat transfer by both the rods is identical. The heat transfer by both the rods is the same:
(k₁A(T₁ – T)) / L = (k₂A(T – T₂)) / L
where:
– k₁ and k₂ are the thermal conductivities of the first and second rods,
– T₁ and T₂ are the temperatures at the free ends of the first and second rods
– T is the temperature at the junction.
Given:
– The ratio of thermal conductivity is k₁ : k₂ = 5 : 3,
– T₁ = 100°C,
– T₂ = 20°C.
The thermal resistance (R) of a rod is given as: R = L / (kA) where: L is the length of the rod, k is the thermal conductivity, A is the cross-sectional area. Given two rods made of different materials, having equal thermal resistance: R₁ = R₂, and the area of cross-section: A₁ = A₂, we obtain: L₁ /Read more
The thermal resistance (R) of a rod is given as:
R = L / (kA)
where:
L is the length of the rod,
k is the thermal conductivity,
A is the cross-sectional area.
Given two rods made of different materials, having equal thermal resistance: R₁ = R₂, and the area of cross-section: A₁ = A₂, we obtain:
L₁ / (k₁A) = L₂ / (k₂A)
Area of cross-section cancels out:
L₁ / k₁ = L₂ / k₂
Rearranging to get the ratio of lengths:
L₁ / L₂ = k₁ / k₂
k₁ : k₂ = 5 : 4
L₁ : L₂ = 4 : 5
Answer: 4 : 5
We have to calculate the heat capacity of both bodies and compare the initial temperatures to determine which way the heat will flow. The formula for heat capacity (C) is: C = m × s where: m = mass, s = specific heat. Body A: Cₐ = 0.5 × 0.85 = 0.425 Body B: C_b = 0.3 × 0.9 = 0.27 The body having a hRead more
We have to calculate the heat capacity of both bodies and compare the initial temperatures to determine which way the heat will flow.
The formula for heat capacity (C) is:
C = m × s
where:
m = mass,
s = specific heat.
Body A:
Cₐ = 0.5 × 0.85 = 0.425
Body B:
C_b = 0.3 × 0.9 = 0.27
The body having a higher product of mass and specific heat will have more thermal energy at the same temperature. However, in this case, the temperature plays a major role in deciding where the direction of heat will be.
Initial temperatures:
– A = 60°C
– B = 90°C
As body B has a higher temperature than body A, the heat will flow from B to A.
To cause heat to move from one end of a solid to another, there must exist a temperature gradient. This would mean that two parts of the solid must differ in temperature as heat flows from the region with higher temperature towards the region of lower temperature. Click here for more: https://www.tiRead more
To cause heat to move from one end of a solid to another, there must exist a temperature gradient. This would mean that two parts of the solid must differ in temperature as heat flows from the region with higher temperature towards the region of lower temperature.
The energy radiated by a body is given by the Stefan-Boltzmann law: E ∝ T⁴ where E is the energy emitted and T is the temperature in Kelvin. To find the ratio of the energies emitted at two temperatures, we use the formula: (E₂ / E₁) = (T₂ / T₁)⁴ First, convert the temperatures from Celsius to KelviRead more
The energy radiated by a body is given by the Stefan-Boltzmann law:
E ∝ T⁴
where E is the energy emitted and T is the temperature in Kelvin.
To find the ratio of the energies emitted at two temperatures, we use the formula:
(E₂ / E₁) = (T₂ / T₁)⁴
First, convert the temperatures from Celsius to Kelvin:
T₁ = 27 + 273 = 300 K T₂ = 92.7 + 273 = 365.7 K
A perfectly black body is one whose absorptive power is 1. This means it absorbs all the radiation incident upon it, without reflecting or transmitting any. A black body also emits radiation at maximum efficiency for any given temperature. Click here for more: https://www.tiwariacademy.com/ncert-solRead more
A perfectly black body is one whose absorptive power is 1. This means it absorbs all the radiation incident upon it, without reflecting or transmitting any. A black body also emits radiation at maximum efficiency for any given temperature.
In any movement of a body under the effect of a force, work is done and the amount depends upon the force, distance covered and angle between force and direction. Here it is given that a body moves 10 m under the influence of a 10 N force and the amount of work is 25 Joules. We establish the angle mRead more
In any movement of a body under the effect of a force, work is done and the amount depends upon the force, distance covered and angle between force and direction. Here it is given that a body moves 10 m under the influence of a 10 N force and the amount of work is 25 Joules.
We establish the angle made between the force and the direction of motion for us to deduce the relation between these parameters. Work done is essentially a product of force, displacement, and the cosine of the angle between them. In this context, work done here is lesser than the maximum possible work which would have occurred if the force had acted in full in the direction of motion. This means that the force is not completely aligned with the motion. A part of the force works in doing work while the other part of it is perpendicular to the motion.
From the values above, we find that the angle between the force and motion is 60 degrees. Thus, this force is partially effective in causing displacement; its directional component is the cause of the work done. This example goes to prove that the angle determines work.
Let us determine the center of mass's speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.Read more
Let us determine the center of mass’s speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.
In the initial state, both particles are at rest and therefore have zero initial momentum. As they start moving toward one another, acceleration occurs due to the mutual gravitational attraction between the particles. The velocity of the center of mass is the main concept in this scenario, representing the overall motion of the system based on individual masses and their respective velocities.
Despite the fact that the particles are accelerating as they approach each other, the principle of conservation of momentum states that the center of mass is unchanged. The relative motion of the two particles will affect the center of mass, and since they are moving toward each other, the center of mass remains stationary. Thus, the effect of their combined motion is to produce no overall acceleration in the center of mass. Therefore, the speed of the center of mass of this system is zero, meaning that the motion of the individual particles does not alter the overall state of rest of the system.
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces theRead more
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces the distribution. This is important in executing rotations properly during the dive.
This process involves the conservation of angular momentum. In the absence of an external torque on a system, the angular momentum is constant. By reducing the moment of inertia, the diver automatically increases their angular velocity, allowing for faster rotations. This technique is necessary to complete complex aerial maneuvers such as somersaults and twists within the short time available in the air.
Before diving, the diver tucks into an acock position so that rotation can take place rapidly, but at close proximity to the water edge, they extend their body, increasing the moment of inertia in order to bridle the speed of rotation, allowing for entry into the pool safely and precisely while minimizing splash and inflicting damage. This way, bending the head and body is essential for divers to achieve maximum rotational motion and execute complicated maneuvers with great accuracy.
The unit is called the Joule second (J·s), and it's used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body's rotational inertia and its angular velocity. Stated another way, it gives a measurRead more
The unit is called the Joule second (J·s), and it’s used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body’s rotational inertia and its angular velocity. Stated another way, it gives a measure of how much motion an object possesses and how it’s distributed around the axis of rotation.
Angular momentum is applied to describe motion systems in the physical world, including spinning objects, rotating planets, and even quantum systems. In this case, the unit would be Joule second because it involves quantities like torque and time, which together reflect aspects of energy and motion in rotational contexts.
All the other quantities of the given choices are measured in totally different units. Linear momentum is measured in kilogram meter per second, work is measured in Joules, and pressure is measured in Pascal. The units also fit with the physical definitions and the mathematical formulation of the quantities concerned.
Accordingly, in the following set of choices, angular momentum would be measured in Joule seconds, presenting the uniqueness with respect to quantities for rotational motion study.
Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined end to end. If the temperature of the free end of the first rod is 100°C and free end of the second rod is 20°C, then the temperature of the jucntion is
We can solve this problem using the formula for heat transfer through a rod, which is as follows: Q = (kA(T₁ - T₂)) / L where: - Q is the heat transferred, - k is the thermal conductivity, - A is the cross-sectional area, - (T₁ - T₂) is the temperature difference, - L is the length of the rod. SinceRead more
We can solve this problem using the formula for heat transfer through a rod, which is as follows:
Q = (kA(T₁ – T₂)) / L
where:
– Q is the heat transferred,
– k is the thermal conductivity,
– A is the cross-sectional area,
– (T₁ – T₂) is the temperature difference,
– L is the length of the rod.
Since the rods are connected end to end, heat transfer by both the rods is identical. The heat transfer by both the rods is the same:
(k₁A(T₁ – T)) / L = (k₂A(T – T₂)) / L
where:
– k₁ and k₂ are the thermal conductivities of the first and second rods,
– T₁ and T₂ are the temperatures at the free ends of the first and second rods
– T is the temperature at the junction.
Given:
– The ratio of thermal conductivity is k₁ : k₂ = 5 : 3,
– T₁ = 100°C,
– T₂ = 20°C.
Now, equating the heat transfer in both rods:
(5(100 – T)) / 3 = (T – 20)
Solving for T:
5(100 – T) = 3(T – 20)
500 – 5T = 3T – 60
500 + 60 = 8T
560 = 8T
T = 70°C
Hence, the temperature at the junction is 70°C.
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The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio
The thermal resistance (R) of a rod is given as: R = L / (kA) where: L is the length of the rod, k is the thermal conductivity, A is the cross-sectional area. Given two rods made of different materials, having equal thermal resistance: R₁ = R₂, and the area of cross-section: A₁ = A₂, we obtain: L₁ /Read more
The thermal resistance (R) of a rod is given as:
R = L / (kA)
where:
L is the length of the rod,
k is the thermal conductivity,
A is the cross-sectional area.
Given two rods made of different materials, having equal thermal resistance: R₁ = R₂, and the area of cross-section: A₁ = A₂, we obtain:
L₁ / (k₁A) = L₂ / (k₂A)
Area of cross-section cancels out:
L₁ / k₁ = L₂ / k₂
Rearranging to get the ratio of lengths:
L₁ / L₂ = k₁ / k₂
k₁ : k₂ = 5 : 4
L₁ : L₂ = 4 : 5
Answer: 4 : 5
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A body A of mass 0.5 kg and specific heat 0.85 is at a temperature of 60°C. Another body B of mass 0.3 kg and specific heat 0.9 is at a temperature of 90°C. When they are connected to a conducting rod, heat will flow from
We have to calculate the heat capacity of both bodies and compare the initial temperatures to determine which way the heat will flow. The formula for heat capacity (C) is: C = m × s where: m = mass, s = specific heat. Body A: Cₐ = 0.5 × 0.85 = 0.425 Body B: C_b = 0.3 × 0.9 = 0.27 The body having a hRead more
We have to calculate the heat capacity of both bodies and compare the initial temperatures to determine which way the heat will flow.
The formula for heat capacity (C) is:
C = m × s
where:
m = mass,
s = specific heat.
Body A:
Cₐ = 0.5 × 0.85 = 0.425
Body B:
C_b = 0.3 × 0.9 = 0.27
The body having a higher product of mass and specific heat will have more thermal energy at the same temperature. However, in this case, the temperature plays a major role in deciding where the direction of heat will be.
Initial temperatures:
– A = 60°C
– B = 90°C
As body B has a higher temperature than body A, the heat will flow from B to A.
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In order that the heat flows from one part of a solid to another part, what is required?
To cause heat to move from one end of a solid to another, there must exist a temperature gradient. This would mean that two parts of the solid must differ in temperature as heat flows from the region with higher temperature towards the region of lower temperature. Click here for more: https://www.tiRead more
To cause heat to move from one end of a solid to another, there must exist a temperature gradient. This would mean that two parts of the solid must differ in temperature as heat flows from the region with higher temperature towards the region of lower temperature.
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If a body is heated from 27° C to 92.7 °C, then the ratio of their energies of radiations emitted will be
The energy radiated by a body is given by the Stefan-Boltzmann law: E ∝ T⁴ where E is the energy emitted and T is the temperature in Kelvin. To find the ratio of the energies emitted at two temperatures, we use the formula: (E₂ / E₁) = (T₂ / T₁)⁴ First, convert the temperatures from Celsius to KelviRead more
The energy radiated by a body is given by the Stefan-Boltzmann law:
E ∝ T⁴
where E is the energy emitted and T is the temperature in Kelvin.
To find the ratio of the energies emitted at two temperatures, we use the formula:
(E₂ / E₁) = (T₂ / T₁)⁴
First, convert the temperatures from Celsius to Kelvin:
T₁ = 27 + 273 = 300 K T₂ = 92.7 + 273 = 365.7 K
Now, find the ratio:
(E₂ / E₁) = (365.7 / 300)⁴ ≈ (1.219)⁴ ≈ 2.1⁴ ≈ 16
So, the ratio of the energies emitted is 1 : 16.
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A perfectly black body is one whose
A perfectly black body is one whose absorptive power is 1. This means it absorbs all the radiation incident upon it, without reflecting or transmitting any. A black body also emits radiation at maximum efficiency for any given temperature. Click here for more: https://www.tiwariacademy.com/ncert-solRead more
A perfectly black body is one whose absorptive power is 1. This means it absorbs all the radiation incident upon it, without reflecting or transmitting any. A black body also emits radiation at maximum efficiency for any given temperature.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
A body moves a distance of 10 m under the action of force F = 10N. If the work done is 25J, the angle which the force makes with the direction of motion is
In any movement of a body under the effect of a force, work is done and the amount depends upon the force, distance covered and angle between force and direction. Here it is given that a body moves 10 m under the influence of a 10 N force and the amount of work is 25 Joules. We establish the angle mRead more
In any movement of a body under the effect of a force, work is done and the amount depends upon the force, distance covered and angle between force and direction. Here it is given that a body moves 10 m under the influence of a 10 N force and the amount of work is 25 Joules.
We establish the angle made between the force and the direction of motion for us to deduce the relation between these parameters. Work done is essentially a product of force, displacement, and the cosine of the angle between them. In this context, work done here is lesser than the maximum possible work which would have occurred if the force had acted in full in the direction of motion. This means that the force is not completely aligned with the motion. A part of the force works in doing work while the other part of it is perpendicular to the motion.
From the values above, we find that the angle between the force and motion is 60 degrees. Thus, this force is partially effective in causing displacement; its directional component is the cause of the work done. This example goes to prove that the angle determines work.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be
Let us determine the center of mass's speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.Read more
Let us determine the center of mass’s speed as it moves toward one another due to their mutual attraction since two particles initially are at rest. We may regard the individual speeds of the particles as they move toward each other. One of them is moving at a speed v, and the other at the speed 2v.
In the initial state, both particles are at rest and therefore have zero initial momentum. As they start moving toward one another, acceleration occurs due to the mutual gravitational attraction between the particles. The velocity of the center of mass is the main concept in this scenario, representing the overall motion of the system based on individual masses and their respective velocities.
Despite the fact that the particles are accelerating as they approach each other, the principle of conservation of momentum states that the center of mass is unchanged. The relative motion of the two particles will affect the center of mass, and since they are moving toward each other, the center of mass remains stationary. Thus, the effect of their combined motion is to produce no overall acceleration in the center of mass. Therefore, the speed of the center of mass of this system is zero, meaning that the motion of the individual particles does not alter the overall state of rest of the system.
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A diver in a swimming pool bends his head before diving. It
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces theRead more
When a diver flexes his or her head and tucks the limbs before making a dive, he or she reduces his or her moment of inertia. Moment of inertia is defined as the mass distribution around an axis of rotation. Since the diver draws his or her mass closer to the axis of rotation, he or she reduces the distribution. This is important in executing rotations properly during the dive.
This process involves the conservation of angular momentum. In the absence of an external torque on a system, the angular momentum is constant. By reducing the moment of inertia, the diver automatically increases their angular velocity, allowing for faster rotations. This technique is necessary to complete complex aerial maneuvers such as somersaults and twists within the short time available in the air.
Before diving, the diver tucks into an acock position so that rotation can take place rapidly, but at close proximity to the water edge, they extend their body, increasing the moment of inertia in order to bridle the speed of rotation, allowing for entry into the pool safely and precisely while minimizing splash and inflicting damage. This way, bending the head and body is essential for divers to achieve maximum rotational motion and execute complicated maneuvers with great accuracy.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
Joule second is the unit of
The unit is called the Joule second (J·s), and it's used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body's rotational inertia and its angular velocity. Stated another way, it gives a measurRead more
The unit is called the Joule second (J·s), and it’s used to describe angular momentum-a concept in rotational motion. The rotational equivalent of linear momentum, angular momentum is a measure dependent on the body’s rotational inertia and its angular velocity. Stated another way, it gives a measure of how much motion an object possesses and how it’s distributed around the axis of rotation.
Angular momentum is applied to describe motion systems in the physical world, including spinning objects, rotating planets, and even quantum systems. In this case, the unit would be Joule second because it involves quantities like torque and time, which together reflect aspects of energy and motion in rotational contexts.
All the other quantities of the given choices are measured in totally different units. Linear momentum is measured in kilogram meter per second, work is measured in Joules, and pressure is measured in Pascal. The units also fit with the physical definitions and the mathematical formulation of the quantities concerned.
Accordingly, in the following set of choices, angular momentum would be measured in Joule seconds, presenting the uniqueness with respect to quantities for rotational motion study.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/