The acceleration of gravity is 9.81 meters per second squared (m/s2). What is it in units of centimeters per second squared (cm/s2)?
The correct answer and explanation is :
The acceleration due to gravity is typically expressed in meters per second squared (m/s²), but we are asked to convert this to centimeters per second squared (cm/s²). Here’s how we do that:
Step 1: Convert meters to centimeters
We know that 1 meter is equal to 100 centimeters. Therefore, to convert from meters to centimeters, we multiply by 100:
[
1 \text{ meter} = 100 \text{ centimeters}
]
Step 2: Perform the conversion
Since the acceleration of gravity is (9.81 \, \text{m/s}^2), we want to convert this value into cm/s². We do this by multiplying by 100, because we are converting meters to centimeters:
[
9.81 \, \text{m/s}^2 \times 100 = 981 \, \text{cm/s}^2
]
Final Answer:
The acceleration due to gravity, when expressed in centimeters per second squared, is:
[
981 \, \text{cm/s}^2
]
Explanation:
The acceleration due to gravity is a fundamental constant that measures the rate at which objects accelerate towards the Earth’s surface under the influence of gravity. The standard value of (9.81 \, \text{m/s}^2) is based on measurements near Earth’s surface at sea level.
In physics, it’s common to express acceleration in different units depending on the context. The SI unit of acceleration is meters per second squared (m/s²), but sometimes, smaller units such as centimeters per second squared (cm/s²) are preferred, particularly in contexts where more precision is desired at smaller scales.
The conversion process here is simple because it’s based on the relationship between meters and centimeters. Since 1 meter is equivalent to 100 centimeters, converting from meters to centimeters involves multiplying by 100. Thus, the gravity constant expressed in cm/s² is 981 cm/s². This is the same acceleration but scaled to a different unit of measurement.
This conversion is important in contexts where centimeter-level precision is necessary, such as in laboratory experiments or high-precision measurements. It’s an example of how understanding unit conversions is essential for working with physical quantities in different systems of measurement.