Charge is placed on the surface of a 2.7-cm radius isolated conducting sphere. the surface charge density is uniform and has the

Answer can be found in the attached document.

A reactant is any substance that takes part in a chemical reaction. Conversely, a product is what emerges from the chemical transformation. A familiar example of a chemical change is rust formation. In this reaction, oxygen and iron, which serve as the reactants, react to produce a substance known as iron oxide, or rust.

Answer:

The mass of the child is 14.133 kg

Explanation:

According to the principle of linear momentum conservation, we get;

(m₁ + m₂) × v₁ + m₃ × v₂ = (m₁ + m₂) × v₃ - m₃ × v₄

The negative sign signifies that their velocities were directed oppositely

Considering both the child and the ball are initially at rest, we have;

v₁ = 0 m/s and v₂= 0 m/s

Thus;

0 = m₁ × v₃ - m₂ × v₄

(m₁ + m₂) × v₃ = m₃ × v₄

Where:

m₁ = Mass of the child

m₂ = Mass of the scooter = 2.4 kg

v₃ = Final velocity of the child and scooter = 0.45 m/s

m₃ = Mass of the ball = 2.4 kg

v₄ = Final velocity of the ball = 3.1 m/s

Substituting the known values gives us;

(m₁ + 2.4) × 0.45 = 2.4 × 3.1

(m₁ + 2.4) = 16.533

This implies m₁ + 2.4 = 16.533

Thus, m₁ = 16.533 - 2.4 = 14.133 kg

The mass of the child equals 14.133 kg.

Response:

Explanation:

Let T denote the tension.

By employing Newton's second law to analyze the bucket's downward motion, we have:

mg - T = ma

A torque, TR, acts on the drum, inducing an angular acceleration α in it. If I refers to the moment of inertia of the drum, then:

TR = Iα

Rearranging gives: TR = Ia/R

This leads to T =  Ia/R²

Substituting this expression for T back into the previous equation yields:

mg - T = ma

mg - Ia/R² = ma

Consequently, we find that mg =  Ia/R² + ma

Therefore, a (I/R² + m) = mg

This results in: a = mg / (I/R² + m)

Next, we aim to express T as:

mg - T = ma

which simplifies to mg - ma  = T

Rearranging gives mg - m²g / (I/R² + m) = T

Thus, we arrive at: mg - mg / (1 + I / m R²) = T

For part (b), T =  Ia/R²

and for part (c), the moment of inertia of a hollow cylinder calculates to:

I = 1/2  M (R² - (R² / 4))

This simplifies to 3/4 x 1/2 MR², yielding 3/8 MR²

Thus, I / R² = 3/8 M

When we substitute, we find a = mg / (3/8 M + m)

and subsequently T =  Ia/R²

= 3/8 MR² × mg / (3/8 M + m) × 1/R²

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