What is the weight of the mass (100g) in Newtons? Show calculation.
The Correct Answer and Explanation is:
Correct Answer:
To convert the mass of 100 grams to weight in Newtons, we use the formula:Weight (W)=mass (m)×gravitational acceleration (g)\text{Weight (W)} = \text{mass (m)} \times \text{gravitational acceleration (g)}Weight (W)=mass (m)×gravitational acceleration (g)
Where:
- Mass m=100 g=0.1 kgm = 100 \, \text{g} = 0.1 \, \text{kg}m=100g=0.1kg
- Gravitational acceleration g=9.8 m/s2g = 9.8 \, \text{m/s}^2g=9.8m/s2
Now calculate:W=0.1 kg×9.8 m/s2=0.98 NW = 0.1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 0.98 \, \text{N}W=0.1kg×9.8m/s2=0.98N
Final Answer: 0.98 Newtons
Explanation:
Weight is a measure of the force exerted by gravity on a mass. While mass remains constant no matter where an object is in the universe, weight depends on the gravitational pull acting on it. On Earth, this acceleration due to gravity is approximately 9.8 meters per second squared.
To find the weight of an object, we multiply its mass (in kilograms) by the gravitational acceleration. The unit of weight in the International System of Units (SI) is the Newton, symbolized as “N”. One Newton is defined as the force needed to accelerate a one-kilogram mass by one meter per second squared.
In this case, we are given a mass of 100 grams. However, the SI unit of mass is the kilogram, so we must first convert grams to kilograms. There are 1000 grams in one kilogram. Therefore, 100 grams is equal to 0.1 kilograms.
After converting the mass, we apply the formula Weight=mass×gravity\text{Weight} = \text{mass} \times \text{gravity}Weight=mass×gravity. Multiplying 0.1 kilograms by 9.8 meters per second squared gives us 0.98 Newtons.
This value means that the Earth exerts a gravitational force of 0.98 Newtons on a 100-gram object. This force is what gives the object its “weight” when measured by a scale on Earth. If the same object were taken to the Moon, where gravity is weaker, it would weigh less even though its mass remains the same.
