Difference between fundamental quantity and derived quantity?

if the mass of the solid body is doubled it density ____________.

if the volume of the solid body is reduced to half, then its desity ________________.

the mass of a solid iron cube of side 4cm is to be determiined. four spring balances is available which is best suited and why ?

a) range 0 - 100g and least count 1g

b) range 0 - 100g, least count 5g

c) 0 - 1000g , least count is 10 g

d) 0- 1000g, least count 25g

Q - A boat floats on water with 3/4 th of its volume inside water, density of water is 10, 000 kg/m3 the density of the material of the boat is _____________________. How?

Q - density of a block of wood which floats on water with 0.1 of its volume avove water is _____________. How?

Explain last questions

## EXPERT ANSWER

Fundamental quantities are those which are the most basic quantities in nature and cannot be derived. Example: Length, Mass, Time etc. You cannot derive them from other quantities.

Derived quantities are those which can be derived from the fundamental quantities. Example: Seed is a derived quantity. It can be derived from fundamental quantities length and time.

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Density = mass/volume

If the mass of the solid body is doubled its density will ** double **. (Considering the solid to be compressible this answer is valid, in case the solid is incompressible the density will remain same)

If the volume of the solid body is reduced to half, then its density will ** double **. (Considering the solid to be compressible this answer is valid, in case the solid is incompressible the density will remain same)

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The mass of a solid iron cube of side 4cm is to be determined. Four spring balances is available which is best suited:

Density of iron is, 7.8 g/cc

Volume of the 4 cm cube is, 64 cc

The mass of the cube = 64 X 7.8 = 499.8 g

Therefore, 0 - 1000g , least count is 10 g will be the best option.

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A boat floats on water with 3/4^{th} of its volume inside water, density of water is 1000 kg/m^{3} the density of the material of the boat is_________?

Let V be the volume of the boat and q be the density of the material of the boat. Weight of the boat is, W = Vqg

Weight of the water displaced, B = ¾ V X 1000 X g

For floatation,

Vqg = ¾ V X 1000 X g

= > q = 750 kg/m^{3}

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Density of a block of wood which floats on water with 0.1 of its volume above water is ________?

Let V be the volume of the wood and q be the density. 0.1 of its volume is above water, which means 0.9 V is below water level.

Weight of the wood, W = Vqg

Weight of water displaced, B = 0.9 X 1000 X g

For floatation,

Vqg = .9 X 1000 X g

= > q = 900 kg/m^{3}

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