Let represent the density of aluminium and that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius on an equal-arm balance.
The radius of aluminum sphere is .
The density of aluminium is
The mass of iron is .
The density is the ratio of the mass of an object tothe unit volume of the space. It describes the heavier or lighter among the different objects.
The volume of the aluminum sphere is given by
The volume of the iron sphere is given by
The condition for the equal-arm balanceis given by
Substitute all the values in the above equation.
Therefore, the radius of the aluminum sphere that satisfies the equal-armbalance criterion is .
Figure on page shows students studying the thermal conduction of energy into cylindrical blocks of ice. As we will see in Chapter , this process is described by the equation
For experimental control, in one set of trials, all quantities except and are constant.
(a) If is made three times larger, does the equation predict that will get larger or get smaller? By what factor?
(b) What pattern of proportionality of to does the equation predict?
(c) To display this proportionality as a straight line on a graph, what quantities should you plot on the horizontal and vertical axes?
(d) What expression represents the theoretical slope of this graph?
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