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If the radius of a rotating disc is doubled while keeping its mass constant, how does its moment of inertia about its axis change?
The moment of inertia of a disc is 𝐼 = 1/2𝑀𝑅². If 𝑅 is doubled, 𝐼 ∝ 𝑅², so it increases by a factor of 4. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of Particle and Rotational motion. Give answer according to your understanding. For more please visit hereRead more
The moment of inertia of a disc is 𝐼 = 1/2𝑀𝑅². If 𝑅 is doubled, 𝐼 ∝ 𝑅², so it increases by a factor of 4. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of Particle and Rotational motion. Give answer according to your understanding.
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Define bulk modulus of elasticity. Give its units and dimensions.
Definition of Bulk Modulus of Elasticity: The bulk modulus of elasticity is the coefficient of a medium's resistance toward uniform compression, defined as a ratio of relative change in volume to the intensity of pressure by which the material volume is decreased or increased. For mathematical expreRead more
Definition of Bulk Modulus of Elasticity:
The bulk modulus of elasticity is the coefficient of a medium’s resistance toward uniform compression, defined as a ratio of relative change in volume to the intensity of pressure by which the material volume is decreased or increased. For mathematical expression the following is employed:
K=-ΔP/(ΔV\V)
where K is the bulk modulus ΔP is the change in pressure ΔV is the change in volume and V is the original volume.
Units:
The SI unit of bulk modulus is Pascal (Pa), which is equal to Newton per square meter (N/m²).
Dimensions:
The dimensions of bulk modulus are expressed as [M L⁻¹ T⁻²], where M is mass L is length and T is time.
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Define modulus of elasticity. Give its units and dimensions. What are different types of moduli of elasticity?
Definition of Modulus of Elasticity: Modulus of elasticity is a measure of the ability of a material to deform elastically under the influence of a force. It is a measure of the ratio of stress (force per unit area) to strain (deformation) in a material. The modulus indicates how much a material wilRead more
Definition of Modulus of Elasticity:
Modulus of elasticity is a measure of the ability of a material to deform elastically under the influence of a force. It is a measure of the ratio of stress (force per unit area) to strain (deformation) in a material. The modulus indicates how much a material will deform under a given load.
Units:
The SI unit of modulus of elasticity is Pascal (Pa), which is equal to Newton per square meter (N/m²).
Dimensions:
The modulus of elasticity is expressed in units of [M L⁻¹ T⁻²], where M stands for mass, L for length, and T for time.
Some Common Moduli of Elasticity:
1. Young’s Modulus (E): It is the tensile or compressive elasticity of a material, that is, the ratio of tensile stress to tensile strain.
2. Bulk Modulus (K): It represents the resistance offered by a material to uniform compression. It is defined as the ratio of the change in pressure to the relative decrease in volume.
3. Shear Modulus (G): Also known as the modulus of rigidity, it measures a material’s response to shear stress. It is defined as the ratio of shear stress to shear strain.
4. Poisson’s Ratio (ν): It is a measure of the ratio of transverse strain to axial strain in a material subjected to axial stress, but not a modulus in the strict sense.
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State Hooke’s law. How can it be verified experimentally?
Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as: F = -kx where F is the restoring force exerted by the spring k is the spring constant andRead more
Hooke’s Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as:
F = -kx
where F is the restoring force exerted by the spring k is the spring constant and x is the displacement from the equilibrium position.
Experimental Verification:
To verify Hooke’s Law experimentally, the following steps can be followed:
1. Setup: Attach a spring vertically to a fixed support and hang weights from the free end of the spring. Use a ruler or measuring tape to measure the displacement.
2. Apply Weights: Gradually add known weights to the spring and measure the extension (displacement) of the spring each time a weight is added. Ensure that the weights are added incrementally and the spring is not overstretched.
3. Record Data: Record the weight applied (force) and the corresponding displacement of the spring.
4. Plotting Graph: Plot a graph of the applied force (y-axis) against the displacement (x-axis). According to Hooke’s Law, the graph should be a straight line passing through the origin, indicating that the force is directly proportional to the displacement.
5. Determine the Spring Constant: The slope of the linear graph gives the value of the spring constant (k), confirming the validity of Hooke’s Law.
By conducting this experiment, one can observe that the extension of the spring is proportional to the applied force, thereby verifying Hooke’s Law.
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A thin ring of radius 𝑅 and mass 𝑀 rotates about an axis passing through its diameter. What is its moment of inertia?
The moment of inertia of a thin ring about a diameter is 𝐼 = 1/2MR² , as derived using the perpendicular axis theorem. This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of particle and Rotational motion. Give answer according to your understanding. For more pleaRead more
The moment of inertia of a thin ring about a diameter is 𝐼 = 1/2MR² , as derived using the perpendicular axis theorem.
This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of particle and Rotational motion. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/