Acceleration due to gravity, g = 9.81 m/s
unless otherwise specified Density of water = 1,000 kg/m
The Correct Answer and Explanation is:
The acceleration due to gravity, commonly represented as g, is 9.81 meters per second squared (m/s²). This value is typically used in calculations unless stated otherwise.
The density of water is 1,000 kilograms per cubic meter (kg/m³) under standard conditions, such as at 4°C and 1 atmosphere of pressure.
Explanation
Acceleration due to gravity is a fundamental concept in physics, particularly in mechanics. It represents the rate at which objects accelerate toward the Earth when dropped, assuming there is no air resistance. The standard value of 9.81 m/s² is derived from Earth’s average gravitational pull at sea level. This value means that for every second an object is falling freely, its velocity increases by 9.81 meters per second.
This constant is important in a wide range of physics problems. For instance, when calculating the force of an object using Newton’s Second Law (F = ma), the acceleration “a” becomes 9.81 m/s² if the force is due to gravity. So the weight of an object is calculated by multiplying its mass by 9.81 m/s². For example, an object with a mass of 10 kilograms has a weight of 10 × 9.81 = 98.1 newtons.
The density of water, defined as mass per unit volume, is a critical value in fluid mechanics, chemistry, and environmental science. Its standard value is 1,000 kg/m³, meaning that a volume of one cubic meter of water has a mass of 1,000 kilograms. This value is especially important in calculations involving buoyancy and fluid pressure.
For example, to calculate the pressure at a certain depth in water, the formula used is:
Pressure = density × gravity × height, or P = ρgh
Using standard values:
P = 1,000 kg/m³ × 9.81 m/s² × h
This shows that pressure increases linearly with depth, governed by both the density of the fluid and the acceleration due to gravity.
