The Question is from neet-physics units-and-measurement conversion-of-units-for-one-system-to-another, and it was created by the author SUBHANI

Question

The density of a substance is given as 0.8 g/$cm^3$. Convert this density to kg/$m^3$.

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option C
## CONCEPT FRAMEWORK
	**Primary Concept**: Unit Conversion
	**Related Topics**: Density, Metric System
	**Prerequisites**: Conversion factors between grams and kilograms, and between centimeters and meters.
## SOLUTION PATHWAY
**Given Information**:
	Density = 0.8 g/$cm^3$
	We need to convert to kg/$m^3$
**Method & Steps**:
	1. Convert grams to kilograms:
		Reasoning: There are 1000 grams in 1 kilogram.
		Formula/Rule: 1 kg = 1000 g, therefore 1 g = 1/1000 kg
	2. Convert cubic centimeters to cubic meters:
		Reasoning: There are 100 centimeters in 1 meter, so 1 $cm^3$ = $(1/100)^3 m^3$ = 1/$10^6$ $m^3$
		Formula/Rule: 1 m = 100 cm, therefore 1 $cm^3$ = $(1/100 m)^3$ = 1/$10^6$ $m^3$
	3. Perform the conversion:
		Working: 0.8 g/$cm^3$ = 0.8 * (1/1000 kg) / (1/$10^6$ $m^3$) = 0.8 * (1/$10^3$) kg / (1/$10^6$ $m^3$) = 0.8 * ($10^6$/$10^3$) kg/$m^3$ = 0.8 * 1000 kg/$m^3$
		Key Point:  When converting from smaller units to larger units, you divide. When converting from smaller units to larger units in the denominator, you multiply.
	4. Calculate the final result:
		Result: 0.8 * 1000 = 800 kg/$m^3$
		Verification: The answer is reasonable because $m^3$ is a much larger volume than $cm^3$ and kg is a much larger mass than g.
 ## OPTION ANALYSIS
[A] :x:  Incorrect. This would be correct if the answer was only converting g to kg, not cm^3 to m^3.
[B] :x: Incorrect. This is off by a factor of 10.
[C] ✓: Correct. 0.8 g/$cm^3$ is equal to 800 kg/$m^3$.
[D] :x: Incorrect. This is off by a factor of 10.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Forgetting to cube the conversion factor when dealing with volume.  [How to avoid]: Remember that volume is a three-dimensional quantity, so the length conversion factor must be cubed.
		2. [Error 2]:  Incorrectly multiplying or dividing by the conversion factors. [How to avoid]: Set up the conversion as a fraction to make sure units cancel out correctly.
	**Quick Tips**:
		1. [Helpful shortcut]: Remember 1 g/$cm^3$ = 1000 kg/$m^3$. Use this as a reference point for other conversions.
		2. [Memory aid]:  When going from smaller units to larger units (g to kg, cm to m), you will usually be multiplying by a factor greater than one for the numerator and dividing by a factor greater than one for the denominator.

SUBHANI · Answer

8 kg/$m^3$

SUBHANI · Answer

80 kg/$m^3$

SUBHANI · Answer

The correct Option is "800 kg/$m^3$"

SUBHANI · Answer

8000 kg/$m^3$

NEET Physics Units And Measurement Conversion Of Units For One System To Another MCQs

Select Topic

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company