Answer : velocity

[λ]=[L] , [g]=[LT-²]

Therefore, [λg] = [L²T-²]

=> √[λg] = [LT-¹]

which is the dimension of velocity.

Physical Quantity Represented by √λg:

The expression √λg represents the square root of the product of the wavelength (λ) and the acceleration due to gravity (g). It is important to understand the physical significance of each component and how their combination leads to a meaningful physical quantity.

Wavelength (λ):
Wavelength is a fundamental property of waves and is defined as the distance between two consecutive points in a wave that are in phase. It is usually represented by the Greek letter lambda (λ). Wavelength is commonly used to describe various types of waves such as electromagnetic waves (e.g., light) and mechanical waves (e.g., sound).

Acceleration due to Gravity (g):
Acceleration due to gravity represents the acceleration experienced by an object in free fall due to the gravitational force exerted by a massive body. Near the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s². It determines the rate at which objects fall and is responsible for their weight.

Physical Quantity Represented by √λg:
The expression √λg combines the wavelength and the acceleration due to gravity. It represents the velocity of a wave in a gravitational field. This quantity is significant in various scenarios, particularly in the context of gravitational waves and the propagation of waves in different mediums.

Gravitational Waves:
Gravitational waves are ripples in the fabric of spacetime caused by the acceleration of massive objects. They propagate at the speed of light and carry energy away from their source. The expression √λg is related to the velocity of gravitational waves. It indicates how fast these waves travel in a given gravitational field.

Wave Propagation:
In general, waves can propagate through different mediums, such as air, water, or solids. The velocity of a wave in a medium depends on the properties of that medium. However, in the presence of a gravitational field, the effective velocity of a wave is modified due to the influence of gravity. The expression √λg provides a measure of this modified velocity.

In conclusion, √λg represents the square root of the product of the wavelength (λ) and the acceleration due to gravity (g). It is a significant quantity in the context of gravitational waves and the propagation of waves in different mediums, providing insights into the velocity of these waves in a gravitational field.