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The work done by an applied variable force F = x + x³ from x = 0 m to x = 2 m, where x is displacement , is
To calculate the work done by the variable force F = x + x³ over the displacement from x = 0 m to x = 2 m, we use the work integral: Work W = ∫[0 to 2] F(x) dx Where: - F(x) = x + x³ - x₁ = 0, x₂ = 2 Step 1: Set up the integral W = ∫[0 to 2] (x + x³) dx Step 2: Split and evaluate the integral W = ∫[Read more
To calculate the work done by the variable force F = x + x³ over the displacement from x = 0 m to x = 2 m, we use the work integral:
Work W = ∫[0 to 2] F(x) dx
Where:
– F(x) = x + x³
– x₁ = 0, x₂ = 2
Step 1: Set up the integral
W = ∫[0 to 2] (x + x³) dx
Step 2: Split and evaluate the integral
W = ∫[0 to 2] x dx + ∫[0 to 2] x³ dx
1. For ∫[0 to 2] x dx:
∫ x dx = (1/2) x² |[0 to 2] = (1/2) (2²) – (1/2) (0²) = 2
2. For ∫[0 to 2] x³ dx:
∫ x³ dx = (1/4) x⁴ |[0 to 2] = (1/4) (2⁴) – (1/4) (0⁴) = (16/4) – 0 = 4
Step 3: Add the results
W = 2 + 4 = 6 J
Final Answer:
The work done by the variable force is 6 J.
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The coefficient of restitute, e, for a perfectly elastic collision is?
The coefficient of restitution, e, is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding objects. For a perfectly elastic collision, the kinetic energy and momentum are conserved, and the objects rebound without any loss of energy.Read more
The coefficient of restitution, e, is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding objects.
For a perfectly elastic collision, the kinetic energy and momentum are conserved, and the objects rebound without any loss of energy. Therefore, the coefficient of restitution for a perfectly elastic collision is:
e = 1
Final Answer:
The coefficient of restitution, e, for a perfectly elastic collision is 1.
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For a simple microscope would you prefer a lens of higher focal length or smaller focal length Why?
For a simple microscope, a lens with a smaller focal length is preferred. It provides greater magnification by allowing the image to form closer to the eye, making objects appear larger and more detailed. For more visit here: https://www.tiwariacademy.com/ncert-solutions/class-12/physics/chapter-9/
For a simple microscope, a lens with a smaller focal length is preferred. It provides greater magnification by allowing the image to form closer to the eye, making objects appear larger and more detailed.
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Define the term threshold frequency, in the context of photoelectric emission.
Threshold frequency is the minimum frequency of light required to eject electrons from a material’s surface in the photoelectric effect. Below this frequency, no electrons are emitted, regardless of the light's intensity, as the energy is insufficient to overcome the material's work function. For moRead more
Threshold frequency is the minimum frequency of light required to eject electrons from a material’s surface in the photoelectric effect. Below this frequency, no electrons are emitted, regardless of the light’s intensity, as the energy is insufficient to overcome the material’s work function.
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A step up transformer converts a low input voltage into a high output voltage. Does it violate law of conservation of energy? Explain.
A step-up transformer does not violate the law of conservation of energy. It increases voltage but decreases current proportionally, ensuring the input and output power (minus losses) remain equal. The total energy is conserved, as transformers efficiently transfer electrical energy without creatingRead more
A step-up transformer does not violate the law of conservation of energy. It increases voltage but decreases current proportionally, ensuring the input and output power (minus losses) remain equal. The total energy is conserved, as transformers efficiently transfer electrical energy without creating or destroying it.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/physics/chapter-7/