This question tests basic knowledge of density and unit conversions, specifically for water. The density of water is a fundamental physical property often used in calculations.
C) 1000 grams — As calculated, 1 liter of water has a mass of 1000 grams (or 1 kilogram) due to its density of 1 g/cm³ or 1 kg/L.
What is the mass of an object with a weight of 50 Newtons on Earth's surface? (Acceleration due to gravity = 9.8 m/s²)
To find the mass of an object given its weight and the acceleration due to gravity, we use the fundamental formula relating weight, mass, and gravitational acceleration: \(W = mg\). We need to rearrange this formula to solve for mass (\(m\)).
The closest option is 5.1 kg.
Correct Option: A) 5.1 kg
The question asks to identify the property of matter that remains constant irrespective of its location in the universe. This requires understanding the definitions of mass, volume, weight, and density, and how they are affected by changes in gravitational force or environmental conditions.
A) Mass — Mass is a measure of the amount of matter in an object. It is an intrinsic property and does not depend on gravitational force or location. An object will have the same mass whether it is on Earth, on the Moon, or in deep space.
The question asks for the weight of an object, not its mass. Mass is an intrinsic property of an object and remains constant regardless of gravity. Weight, however, is the force exerted on an object due to gravity and is calculated using Newton's second law of motion, \(F = ma\), where \(F\) is the force (weight), \(m\) is the mass, and \(a\) is the acceleration due to gravity (\(g\)).
Weight (\(W\)) is the force of gravity acting on an object's mass. It is calculated using the formula:
\[ W = m \times g \]The unit for force (weight) is Newtons (\(\text{N}\)).
Correct Option: B) 98 N
The question asks for the correct relationship between mass (m), volume (V), and density (ρ). Density is a fundamental physical property of matter, defined as the mass per unit volume. Understanding this definition is key to deriving the correct formula.
Correct Option: C) \(V = m / \rho\)
This option correctly represents the relationship where volume is calculated by dividing the mass by the density. This is a direct rearrangement of the fundamental density formula \(\rho = m/V\).
This problem requires us to calculate the volume of an object given its mass and density. We will use the fundamental formula relating mass, density, and volume.
where:
Substitute these values into the rearranged formula:
\[ V = \frac{20 \text{ kg}}{4 \text{ kg/m}^3} \]Correct Option: A) 5 m³ is the correct volume, calculated by dividing the mass by the density.