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REY
1 month ago
5

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1, θ2, and θ3, respectively,

and released. The approximation sin θ = θ holds for all three angles, with θ3 > θ2 > θ1. How do the angular frequencies of the three pendulums compare?
Physics
1 answer:
Sav [3.1K]1 month ago
6 0

Answer:

All three pendulums will have the same angular frequencies.

Explanation:

For a simple pendulum, the time period using the approximation sin(\theta )\approx \thetais expressed as:

T=2\pi\sqrt{\frac{l}{g}}

The angular frequency \omega is defined as

\omega =\frac{2\pi }{T}\\\\\omega =\frac{2\pi}{2\pi \sqrt{\frac{l}{g}}}\\\\\therefore \omega =\sqrt{\frac{g}{l}}

Since the angular frequency remains unaffected by the initial angle (valid strictly for small angle approximations), we deduce that the angular frequencies of the three pendulums are identical.

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If the axes of the two cylinders are parallel, but displaced from each other by a distance d, determine the resulting electric f
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Response:

E =  ρ ( R1²) / 2 ∈o R

Clarification:

Provided information

Two cylinders are aligned parallel

Distance = d

Radial distance = R

d < (R2−R1)

To determine

Express the response using the variables ρE, R1, R2, R3, d, R, and constants

Solution

We have two parallel cylinders

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EA = Q(enclosed) / ∈o......1

Initially, we calculate Q(enclosed) = ρ Volume

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Thus, inserting all values into equation 1

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This simplifies to

E =  ρ ( R1²) / 2 ∈o R

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A square loop of wire with initial side length 10 cm is placed in a magnetic field of strength 1 T. The field is parallel to the
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Answer:

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Explanation:

B = strength of the magnetic field aligning with the loop's axis = 1 T

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E = (1) (20 x 10⁻⁴ )

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The answer is B. Since the first collision is elastic, both momentum and kinetic energy can be conserved within the system. The coefficient of restitution for an elastic collision is one, and it is often referred to as a perfectly elastic collision. Conversely, in a perfectly inelastic collision, kinetic energy is lost as it transforms into another form, such as internal energy. While momentum remains conserved in an inelastic collision, kinetic energy is not.
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