We apply the formula for heat conduction rate to solve this. Q = (kA(T₂ - T₁)) / L Q is the heat conducted per unit time k is the thermal conductivity A is the cross-sectional area (T₂ - T₁) is the temperature difference L is the length of the rod. We are given - The diameters are in the ratio 1:2,Read more
We apply the formula for heat conduction rate to solve this.
Q = (kA(T₂ – T₁)) / L
Q is the heat conducted per unit time
k is the thermal conductivity
A is the cross-sectional area
(T₂ – T₁) is the temperature difference
L is the length of the rod.
We are given
– The diameters are in the ratio 1:2, so the areas A will be in the ratio 1² : 2² = 1:4,
– The lengths are in the ratio 2:1.
We can now compute the ratio of heat conducted through the rods:
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice. The formula to calculate the heat required to melt the ice is: Q = m ⋅ Lբ Where: - Q is the heat lost by the water (in calories), - m is the mass of the ice meRead more
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice.
The formula to calculate the heat required to melt the ice is:
Q = m ⋅ Lբ
Where:
– Q is the heat lost by the water (in calories),
– m is the mass of the ice melted,
– Lբ is the latent heat of fusion of ice (which is 80 cal/g).
The heat gained by the ice is:
Q = m_w ⋅ c_w ⋅ ΔT
Where:
– mᵥᵥ is the mass of water,
– cᵥᵥ is the specific heat capacity of water (which is 1 cal/g°C),
– ΔT is the temperature change of the water (in this case, from 30°C to 0°C, so ΔT = 30°C).
Now, we can calculate the heat gained by the ice:
Q = 80 g ⋅ 1 cal/g°C ⋅ 30°C = 2400 cal
Now, we can find the mass of the ice that melts using the equation for heat required to melt the ice:
In order to solve the problem, we first compute how many apples every businessman purchases and take their difference: 1. Apples purchased by the first businessman: He buys 14 baskets of apples with 425 apples each. Total = 14 x 425 = 5,950 apples. 2. Apples purchased by the second businessman: He bRead more
In order to solve the problem, we first compute how many apples every businessman purchases and take their difference:
1. Apples purchased by the first businessman: He buys 14 baskets of apples with 425 apples each. Total = 14 x 425 = 5,950 apples.
2. Apples purchased by the second businessman: He buys 21 baskets of apples with 295 apples each.
Total = 21 x 295 = 6,195 apples.
3. Difference in apples:
The second businessman buys 6,195 – 5,950 = 245 more apples than the first.
Final Answer:
The second businessman buys 245 more apples than the first.
A rolling sphere without slipping will have the motion of both translational and rotational motion, which are as follows: center of mass, and the rolling around its axis. The kinetic energy of a sphere is found to be both translational as well as rotational. Translational motion depends on its lineaRead more
A rolling sphere without slipping will have the motion of both translational and rotational motion, which are as follows: center of mass, and the rolling around its axis. The kinetic energy of a sphere is found to be both translational as well as rotational. Translational motion depends on its linear velocity while rotational motion is dependent on the angular velocity of the sphere.
The ratio of translational kinetic energy to the total kinetic energy for a rolling sphere is always 10:7. This particular ratio is due to the unique distribution of the sphere’s mass and geometry. A portion of the total energy is dedicated to the translational motion of the center of mass, while the remaining energy contributes to the rotational motion.
Generally, the translational energy is much higher than the rotational energy because the moment of inertia of a sphere is lower compared to the other shapes; hence, the sphere requires much less energy for it to rotate. This way, the rolling motion of the sphere is preserved without slipping.
This ratio is an important concept in physics because it demonstrates the connection between different energies involved in rolling motion. This is particularly helpful in solving problems dealing with energy conservation and dynamics in rolling objects across different surfaces.
The kinetic energy of a rolling body is a combination of translational and rotational. An object that rolls has a linear velocity at its center of mass, as well as rotation about that center. Translational kinetic energy depends on the mass of the object and its velocity. This energy is associated wRead more
The kinetic energy of a rolling body is a combination of translational and rotational. An object that rolls has a linear velocity at its center of mass, as well as rotation about that center. Translational kinetic energy depends on the mass of the object and its velocity. This energy is associated with the motion of the entire body through space.
In addition to translational kinetic energy, the object has rotational kinetic energy because it is rotating about its axis. The amount of rotational energy depends on the moment of inertia of the object, which is a function of the mass distribution and shape of the object and its angular velocity, which is a measure of how fast it is rotating.
When an object rolls without slipping, there is a relationship between its linear velocity and angular velocity. Specifically, the center of mass velocity is directly proportional to the angular velocity of the object. This relationship forms the basis of the understanding for the conservation of energy in rolling motion. Consequently, the total kinetic energy of a rolling body is the sum of its translational and rotational energies, reflecting the movement through space and the rotation about its axis. This total energy is vital in the analysis of the dynamics of rolling objects within different physical settings.
Heat is flowing through the cylindrical rods of the same material. The diameter of the rods are in the ratio 1 : 2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, them the ratio of the amount of heat conducted through them per unit time will be
We apply the formula for heat conduction rate to solve this. Q = (kA(T₂ - T₁)) / L Q is the heat conducted per unit time k is the thermal conductivity A is the cross-sectional area (T₂ - T₁) is the temperature difference L is the length of the rod. We are given - The diameters are in the ratio 1:2,Read more
We apply the formula for heat conduction rate to solve this.
Q = (kA(T₂ – T₁)) / L
Q is the heat conducted per unit time
k is the thermal conductivity
A is the cross-sectional area
(T₂ – T₁) is the temperature difference
L is the length of the rod.
We are given
– The diameters are in the ratio 1:2, so the areas A will be in the ratio 1² : 2² = 1:4,
– The lengths are in the ratio 2:1.
We can now compute the ratio of heat conducted through the rods:
(Q₁ / Q₂) = (A₁ / L₁) × (L₂ / A₂) = (1 / 2) × (4 / 1) = 2
Thus, the ratio of heat conducted through the rods per unit time is 2:1.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-10/
80g of water at 30° C are poured on a large block of ice at 0°C. The mass of ice that melts is
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice. The formula to calculate the heat required to melt the ice is: Q = m ⋅ Lբ Where: - Q is the heat lost by the water (in calories), - m is the mass of the ice meRead more
To solve this problem, we need to use the principle of conservation of energy. The heat lost by the warm water will be used to melt the ice.
The formula to calculate the heat required to melt the ice is:
Q = m ⋅ Lբ
Where:
– Q is the heat lost by the water (in calories),
– m is the mass of the ice melted,
– Lբ is the latent heat of fusion of ice (which is 80 cal/g).
The heat gained by the ice is:
Q = m_w ⋅ c_w ⋅ ΔT
Where:
– mᵥᵥ is the mass of water,
– cᵥᵥ is the specific heat capacity of water (which is 1 cal/g°C),
– ΔT is the temperature change of the water (in this case, from 30°C to 0°C, so ΔT = 30°C).
Now, we can calculate the heat gained by the ice:
Q = 80 g ⋅ 1 cal/g°C ⋅ 30°C = 2400 cal
Now, we can find the mass of the ice that melts using the equation for heat required to melt the ice:
2400 cal = m ⋅ 80 cal/g
m = 2400 / 80 = 30 g
Thus, the mass of ice that melts is 30 g.
See lessMathematics Word problem
In order to solve the problem, we first compute how many apples every businessman purchases and take their difference: 1. Apples purchased by the first businessman: He buys 14 baskets of apples with 425 apples each. Total = 14 x 425 = 5,950 apples. 2. Apples purchased by the second businessman: He bRead more
In order to solve the problem, we first compute how many apples every businessman purchases and take their difference:
1. Apples purchased by the first businessman: He buys 14 baskets of apples with 425 apples each. Total = 14 x 425 = 5,950 apples.
2. Apples purchased by the second businessman: He buys 21 baskets of apples with 295 apples each.
Total = 21 x 295 = 6,195 apples.
3. Difference in apples:
The second businessman buys 6,195 – 5,950 = 245 more apples than the first.
Final Answer:
The second businessman buys 245 more apples than the first.
Click here for more Solutions:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-4/maths/
If a sphere is rolling, the ratio of translational energy to total kinetic energy is given by
A rolling sphere without slipping will have the motion of both translational and rotational motion, which are as follows: center of mass, and the rolling around its axis. The kinetic energy of a sphere is found to be both translational as well as rotational. Translational motion depends on its lineaRead more
A rolling sphere without slipping will have the motion of both translational and rotational motion, which are as follows: center of mass, and the rolling around its axis. The kinetic energy of a sphere is found to be both translational as well as rotational. Translational motion depends on its linear velocity while rotational motion is dependent on the angular velocity of the sphere.
The ratio of translational kinetic energy to the total kinetic energy for a rolling sphere is always 10:7. This particular ratio is due to the unique distribution of the sphere’s mass and geometry. A portion of the total energy is dedicated to the translational motion of the center of mass, while the remaining energy contributes to the rotational motion.
Generally, the translational energy is much higher than the rotational energy because the moment of inertia of a sphere is lower compared to the other shapes; hence, the sphere requires much less energy for it to rotate. This way, the rolling motion of the sphere is preserved without slipping.
This ratio is an important concept in physics because it demonstrates the connection between different energies involved in rolling motion. This is particularly helpful in solving problems dealing with energy conservation and dynamics in rolling objects across different surfaces.
Click here : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessWrite an expression for the kinetic energy of a body rolling without slipping.
The kinetic energy of a rolling body is a combination of translational and rotational. An object that rolls has a linear velocity at its center of mass, as well as rotation about that center. Translational kinetic energy depends on the mass of the object and its velocity. This energy is associated wRead more
The kinetic energy of a rolling body is a combination of translational and rotational. An object that rolls has a linear velocity at its center of mass, as well as rotation about that center. Translational kinetic energy depends on the mass of the object and its velocity. This energy is associated with the motion of the entire body through space.
In addition to translational kinetic energy, the object has rotational kinetic energy because it is rotating about its axis. The amount of rotational energy depends on the moment of inertia of the object, which is a function of the mass distribution and shape of the object and its angular velocity, which is a measure of how fast it is rotating.
When an object rolls without slipping, there is a relationship between its linear velocity and angular velocity. Specifically, the center of mass velocity is directly proportional to the angular velocity of the object. This relationship forms the basis of the understanding for the conservation of energy in rolling motion. Consequently, the total kinetic energy of a rolling body is the sum of its translational and rotational energies, reflecting the movement through space and the rotation about its axis. This total energy is vital in the analysis of the dynamics of rolling objects within different physical settings.
Checkout for more contents: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See less