The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0. The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis. Therefore, the distance of the point (αRead more
The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0.
The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis.
Therefore, the distance of the point (α, β, γ) from the yz-plane is:|α|
The direction cosines of the line are given as: l = 1/√3, m = 1/√6, n = n The angle θ that the line makes with the positive z-axis is related to the direction cosine n by: cos θ = n To find the acute angle, we need to calculate the value of n using the condition that the sum of the squares of the diRead more
The direction cosines of the line are given as:
l = 1/√3, m = 1/√6, n = n
The angle θ that the line makes with the positive z-axis is related to the direction cosine n by:
cos θ = n
To find the acute angle, we need to calculate the value of n using the condition that the sum of the squares of the direction cosines equals 1:
l² + m² + n² = 1
Substituting the values of l and m:
(1/√3)² + (1/√6)² + n² = 1
1/3 + 1/6 + n² = 1
1/2 + n² = 1
n² = 1/2
n = 1/√2
A solid homogeneous sphere of mass and radius is moving on a rough horizontal surface. In this case, the sphere rolls and slides. The dynamics of the sphere are complex because of the interaction between translational and rotational motions. When the sphere moves, it experiences friction from the suRead more
A solid homogeneous sphere of mass and radius is moving on a rough horizontal surface. In this case, the sphere rolls and slides. The dynamics of the sphere are complex because of the interaction between translational and rotational motions. When the sphere moves, it experiences friction from the surface, which affects its motion. Frictional force at the point of contact between the sphere and the surface exerts a torque on the sphere, which is a factor changing the angular momentum of the sphere.
Total kinetic energy is not conserved during this type of motion because part of the energy is converted to heat due to friction. The angular momentum of the sphere about the point of contact with the surface can be conserved. This conservation takes place under certain conditions where no external torques act on the sphere about that particular point. Thus, even as the sphere rolls and slides, the angular momentum can be analyzed effectively using the point of contact as a reference. This situation highlights the interplay between different types of motion and the principles governing angular momentum in systems with friction. This is important to understand in the study of physics and engineering because one needs to know how objects move under various forces.
A solid sphere, disc, and solid cylinder of the same material and mass are allowed to roll down an inclined plane from rest. They will have different motions because their moments of inertia are different. The moment of inertia is a measure of how mass is distributed relative to the axis of rotationRead more
A solid sphere, disc, and solid cylinder of the same material and mass are allowed to roll down an inclined plane from rest. They will have different motions because their moments of inertia are different. The moment of inertia is a measure of how mass is distributed relative to the axis of rotation. Among the three shapes, the solid sphere has the smallest moment of inertia in proportion to its mass; hence, the sphere will accelerate faster than the other two down the incline.
As the shapes roll down the slope, they convert gravitational potential energy into kinetic energy. The solid sphere, with its advantageous distribution of mass, will reach the bottom first, followed by the disc. The disc’s moment of inertia is greater than that of the sphere but smaller than that of the solid cylinder, which means it will accelerate more quickly than the cylinder but not as quickly as the sphere.
The solid cylinder, having the largest moment of inertia, will experience the slowest acceleration and therefore will arrive at the bottom of the incline last. Thus, the solid sphere wins the race down the incline, followed by the disc and then the cylinder.
Here are the key points highlighting the advantages for foreign companies setting up production in India: 1. Vast Market: India offers access to a large consumer base, presenting significant growth opportunities for businesses due to its billion-plus population. 2. Skilled Workforce: Abundance of edRead more
Here are the key points highlighting the advantages for foreign companies setting up production in India:
1. Vast Market: India offers access to a large consumer base, presenting significant growth opportunities for businesses due to its billion-plus population.
2. Skilled Workforce: Abundance of educated and skilled labor at competitive costs, providing efficient manpower for manufacturing and services.
3. Cost-Effectiveness: Lower labor costs compared to many Western countries, contributing to cost-efficient production and competitive pricing.
4. Government Support: Indian government offers incentives like tax breaks, subsidies, and eased regulations to attract foreign investment.
5. Infrastructure Development: Ongoing improvements in infrastructure, logistics, and transportation enhance operational efficiency and distribution networks.
6. Technological Growth: Access to a growing tech industry facilitates technology transfer and innovation, improving production processes.
7. Geographic Advantage: Strategic location providing proximity to emerging markets in Asia, easing access to regional markets.
8. Diverse Industries: India’s diverse economy offers opportunities across various sectors, allowing foreign companies to diversify their investments and operations.
These advantages make India an appealing destination for foreign companies seeking to expand production and capitalize on the country’s economic potential and market size.
Distance of the point (α, β, γ) from yz-plane is
The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0. The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis. Therefore, the distance of the point (αRead more
The yz-plane is defined by the equation x = 0, meaning that for any point on the yz-plane, the x-coordinate is 0.
The distance of a point (α, β, γ) from the yz-plane is the absolute value of its x-coordinate because the yz-plane is perpendicular to the x-axis.
Therefore, the distance of the point (α, β, γ) from the yz-plane is:|α|
Thus, the correct answer is: |α|
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The acute angle which the line with direction cosines 1/√ 3, 1/√ 6, n makes with positive direction of z-axis is
The direction cosines of the line are given as: l = 1/√3, m = 1/√6, n = n The angle θ that the line makes with the positive z-axis is related to the direction cosine n by: cos θ = n To find the acute angle, we need to calculate the value of n using the condition that the sum of the squares of the diRead more
The direction cosines of the line are given as:
l = 1/√3, m = 1/√6, n = n
The angle θ that the line makes with the positive z-axis is related to the direction cosine n by:
cos θ = n
To find the acute angle, we need to calculate the value of n using the condition that the sum of the squares of the direction cosines equals 1:
l² + m² + n² = 1
Substituting the values of l and m:
(1/√3)² + (1/√6)² + n² = 1
1/3 + 1/6 + n² = 1
1/2 + n² = 1
n² = 1/2
n = 1/√2
Thus, cos θ = 1/√2, which gives: θ = π/4
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-11
A solid homogenous sphere of mass M and radius R is moving on rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere
A solid homogeneous sphere of mass and radius is moving on a rough horizontal surface. In this case, the sphere rolls and slides. The dynamics of the sphere are complex because of the interaction between translational and rotational motions. When the sphere moves, it experiences friction from the suRead more
A solid homogeneous sphere of mass and radius is moving on a rough horizontal surface. In this case, the sphere rolls and slides. The dynamics of the sphere are complex because of the interaction between translational and rotational motions. When the sphere moves, it experiences friction from the surface, which affects its motion. Frictional force at the point of contact between the sphere and the surface exerts a torque on the sphere, which is a factor changing the angular momentum of the sphere.
Total kinetic energy is not conserved during this type of motion because part of the energy is converted to heat due to friction. The angular momentum of the sphere about the point of contact with the surface can be conserved. This conservation takes place under certain conditions where no external torques act on the sphere about that particular point. Thus, even as the sphere rolls and slides, the angular momentum can be analyzed effectively using the point of contact as a reference. This situation highlights the interplay between different types of motion and the principles governing angular momentum in systems with friction. This is important to understand in the study of physics and engineering because one needs to know how objects move under various forces.
Click here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then
A solid sphere, disc, and solid cylinder of the same material and mass are allowed to roll down an inclined plane from rest. They will have different motions because their moments of inertia are different. The moment of inertia is a measure of how mass is distributed relative to the axis of rotationRead more
A solid sphere, disc, and solid cylinder of the same material and mass are allowed to roll down an inclined plane from rest. They will have different motions because their moments of inertia are different. The moment of inertia is a measure of how mass is distributed relative to the axis of rotation. Among the three shapes, the solid sphere has the smallest moment of inertia in proportion to its mass; hence, the sphere will accelerate faster than the other two down the incline.
As the shapes roll down the slope, they convert gravitational potential energy into kinetic energy. The solid sphere, with its advantageous distribution of mass, will reach the bottom first, followed by the disc. The disc’s moment of inertia is greater than that of the sphere but smaller than that of the solid cylinder, which means it will accelerate more quickly than the cylinder but not as quickly as the sphere.
The solid cylinder, having the largest moment of inertia, will experience the slowest acceleration and therefore will arrive at the bottom of the incline last. Thus, the solid sphere wins the race down the incline, followed by the disc and then the cylinder.
Click here :
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
What are the advantages to foreign companies in setting up production in India?
Here are the key points highlighting the advantages for foreign companies setting up production in India: 1. Vast Market: India offers access to a large consumer base, presenting significant growth opportunities for businesses due to its billion-plus population. 2. Skilled Workforce: Abundance of edRead more
Here are the key points highlighting the advantages for foreign companies setting up production in India:
1. Vast Market: India offers access to a large consumer base, presenting significant growth opportunities for businesses due to its billion-plus population.
2. Skilled Workforce: Abundance of educated and skilled labor at competitive costs, providing efficient manpower for manufacturing and services.
3. Cost-Effectiveness: Lower labor costs compared to many Western countries, contributing to cost-efficient production and competitive pricing.
4. Government Support: Indian government offers incentives like tax breaks, subsidies, and eased regulations to attract foreign investment.
5. Infrastructure Development: Ongoing improvements in infrastructure, logistics, and transportation enhance operational efficiency and distribution networks.
6. Technological Growth: Access to a growing tech industry facilitates technology transfer and innovation, improving production processes.
7. Geographic Advantage: Strategic location providing proximity to emerging markets in Asia, easing access to regional markets.
8. Diverse Industries: India’s diverse economy offers opportunities across various sectors, allowing foreign companies to diversify their investments and operations.
These advantages make India an appealing destination for foreign companies seeking to expand production and capitalize on the country’s economic potential and market size.
See less