Explanation

 A car radiator is a key component of the engine's cooling system, specifically designed to cool down the engine by transferring heat to the surrounding air. T

Explanation

 In Einstein's universe, the fourth dimension is time. 

Einstein's theory of relativity revolutionized our understanding of space and time, merging them into a single four-dimensional continuum called "spacetime".

Time is considered the fourth dimension within this framework. 

Explanation

The cross product of two vectors A × B ≠ B × A; in fact, A × B = –(B × A), so it is not commutative.

However, it does obey the distributive law over addition, and associative law applies with scalar multiplication but not for three vector cross products.

Explanation

Angular frequency (ω) measures how quickly something moves through an angle in circular motion.

It's given by:

$$omega = frac{2pi}{T} = 2pi f$$

Where:

• $T$ = time period

• $f$= frequency

While it’s also used in oscillations, it is fundamentally defined from circular motion.

Explanation

• The Mole (mol) is the SI unit of amount of substance, representing 6.022 x 10^23 particles.
• It is used to measure the amount of a substance in a sample.

Explanation

 In an isothermal process, the temperature remains constant, so the internal energy of an ideal gas also remains constant.

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

Since the smaller part becomes stationary, it means that the larger part will carry all the momentum.

Let's say the mass of the smaller part is m and the mass of the larger part is 3m.

Initial momentum = Final momentum

mV + 3mV = 3mV'

where V' is the velocity of the larger part.

Combine like terms:

4mV = 3mV'

Divide both sides by 3m:

V' = 4V/3

Explanation

Without an atmosphere to scatter sunlight, there would be no diffusion of light.

Hence, the sky would appear black, just like it does from space.

Explanation