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

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

The degrees of freedom refer to the number of independent ways a gas molecule can store energy.

For a monoatomic gas (e.g., noble gases like helium, neon, argon):

• It has only translational motion along the x, y, and z axes.
• There are no rotational or vibrational degrees of freedom.

Thus, the total degrees of freedom for a monoatomic gas is 3 (one for each spatial direction: x, y, and z).

Explanation

Escape velocity (vₑ) is given by:

vₑ = √(2GM/r)

where:

G = gravitational constant

M = mass of the planet

r = radius of the planet

Given:

M₂ = 1000M₁ (mass of the new planet is 1000 times that of Earth)

r₂ = 10r₁ (radius of the new planet is 10 times that of Earth)

Escape velocity on the new planet (vₑ₂) is:

vₑ₂ = √(2GM₂/r₂)

= √(2G(1000M₁)/(10r₁))

= √(200G(M₁/r₁))

= √200 × √(2GM₁/r₁)

= √200 × vₑ₁

Given vₑ₁ = 11.2 km/s:

vₑ₂ ≈ √200 × 11.2 km/s

≈ 112 km/s

Explanation

Explanation

According to Kepler's third law:

The square of the time period (T²) of a planet.

The Sun is directly proportional to the cube of the semi-major axis (R³) of its orbit.

Mathematically, this can be expressed as:

T² ∝ R³