Explanation

The efficiency of a Carnot engine is defined as the ratio of the heat absorbed from the hot reservoir (heat accepted) to the heat rejected to the cold reservoir (heat rejected).

This efficiency is directly related to the temperature difference between the two reservoirs. 

Explanation

A heat engine operating in reverse is called a heat pump or a refrigerator.

Essentially, these devices move heat from a cooler area to a warmer area, requiring external work to do so, which is the opposite of how a heat engine functions. 

Explanation

The wave velocity in any medium depends on all of the above:

Elasticity:

A medium's elasticity determines how easily it can resist deformation and return to its original shape when force is applied.

Higher elasticity means the wave can travel faster through the medium. 

Density:

The density of a medium also affects wave velocity.

Denser media tend to slow down wave propagation. 

Homogeneity:

A homogeneous medium has consistent properties throughout, meaning the wave velocity will be uniform in all directions. 

Explanation

Speed = 3000 RPM (revolutions per minute)

Step 1: Convert RPM to revolutions per second (RPS)

Step 2: Convert revolutions to radians

Since 1 revolution = 2π radians:

50 rev/sec×2π= 100π radians/sec

Explanation

The ball will fall behind him.

When the man throws the ball vertically upward, it maintains the horizontal velocity of the train due to inertia.

However, the train continues to move forward while the ball is in the air.

As the ball falls back down, it will have traveled a shorter horizontal distance compared to the train,

Resulting in it landing behind the man where he originally threw it. 

Explanation

Momentum (p) is defined as mass (m) multiplied by velocity (v), so p = mv.

If we square p and divide by m, we get: p^2/m = (mv)^2/m = mv^2.

This is the formula for kinetic energy.

Therefore, p^2/m has the same unit as energy. 

Explanation

Refractive index is both unitless and dimensionless. 

Refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in a medium.

Since both speeds have the same units (meters per second),

The units cancel out, making refractive index a dimensionless quantity.

It's also unitless because it doesn't have any associated units

Explanation

The cross product (A × B) is a vector whose magnitude is given by:

| A × B | = |A||B| sinθ

Its direction follows the right-hand rule.

Explanation

Work, mass and distance are scalar quantities because they have magnitude but no direction, but they are not vector quantities.

Vector Quantities: Velocity, momentum, torque, acceleration, weight, displacement.

Scalar Quantities: Work, distance, speed, mass.

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.