# 1.4 Density \$

We must have all noticed that the weight of objects can vary greatly. A plastic teaspoon weighs less than a metal one, and a gold ring weighs twice as much as a silver one, even if the objects are exactly the same size.

The density of a material is a measure of how ‘squashed up’ it is, and a dense object contains more mass than a light object of the same size.

Density  of a substance is defined as its mass per unit volume.

d=M/V

where d– Density, M-mass, and V-volume of the substance.

It is a scalar quantity.

Note that the density of water is $1 g/cm^{3}$, and the rule is that an object of greater density will sink in a liquid of lower density. So, perhaps not surprisingly, the brick will sink in water. But will it sink in mercury? See the table right.

Density of some substances

 Metal or alloy kg/cu.m aluminium – melted 2560 – 2640 aluminium bronze (3-10% Al) 7700 – 8700 aluminium foil 2700 -2750 antifriction metal 9130 -10600 beryllium 1840 beryllium copper 8100 – 8250 brass – casting 8400 – 8700 brass – rolled and drawn 8430 – 8730 bronze – lead 7700 – 8700 bronze – phosphorous 8780 – 8920 bronze (8-14% Sn) 7400 – 8900 cast iron 6800 – 7800 cobolt 8746 copper 8930 delta metal 8600 electrum 8400 – 8900 gold 19320 iron 7850 lead 11340 light alloy based on Al 2560 – 2800 light alloy based on Mg 1760 – 1870 magnesium 1738 mercury 13593 molybdenum 10188 monel 8360 – 8840 nickel 8800 nickel silver 8400 – 8900 platinum 21400 plutonium 19800 silver 10490 steel – rolled 7850 steel – stainless 7480 – 8000 tin 7280 titanium 4500 tungsten 19600 uranium 18900 vanadium 5494 white metal 7100 zinc 7135

Determination of Density of a regular shaped object

1. First weigh the given solid in a physical balance and find its mass m.

2. Then measure the dimensions of the solid with the help of a meter rule (or vernier or micrometer) and calculate its volume V and use the formula

d=M/V

Determination of Density of a irregular shaped solid

1. First weigh the given solid in a physical balance and find its mass

2. Now take a suitable liquid (which does not react with the solid and in which the solid sinks) in a clean measuring cylinder. Note the level of the liquid in the cylinder. Then immerse the given solid completely into the liquid and note the reading again. The difference in the readings give the volume of the solid. Now use the above formula to find its density.

Determination of Density of an irregular shaped solid(Try it now)