Explanation

Explanation

To find the smallest Bragg scattering angle, we can use Bragg's law:

2d sin(θ) = nλ

where d is the distance between the atomic planes, θ is the scattering angle, n is an integer (which is 1 for the smallest angle), and λ is the wavelength of the X-ray.

Given:

d = 0.3 nm

λ = 0.03 nm

Rearranging Bragg's law to solve for θ, we get:

sin(θ) = λ / (2d)

= 0.03 nm / (2 × 0.3 nm)

= 0.05

θ = arcsin(0.05)

≈ 2.9°

Explanation

Explanation

Explanation

To calculate the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a sphere:

I = (2/5)MR^2

where:

I = moment of inertia

M = mass of the Earth (10^25 kg)

R = radius of the Earth (diameter/2 = 12800 km / 2 = 6400 km = 6.4 × 10^6 m)

Plugging in the values, we get:

I = (2/5) × 10^25 kg × (6.4 × 10^6 m)^2

= (2/5) × 10^25 kg × 4.096 × 10^13 m^2

= 1.6384 × 10^38 kg m^2

≈ 1.64 × 10^38 kg m^2

Explanation

Explanation

Explanation

Explanation

Since μ = 1/√3, we can use the fact that μ = tan(θ) when the block just slides down the inclined plane.

μ = 1/√3 = tan(θ)

θ = arctan(1/√3)

θ = 30°

Explanation

When four equal resistors are connected in series, the total resistance (R_total) is:

R_total = 4R

The power dissipated (P) is:

P = V² / R_total

Given P = 10 W, we can rewrite the equation as:

10 = V² / (4R)

Now, if one resistor is connected across the same battery, the power dissipated (P') will be:

P' = V² / R

Comparing the two equations, we can see that:

P' = 4P

= 4 × 10 W

= 40 W