A town is considering building a biodiesel power plant that would burn biomass to generate electricity. Which of the following c
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The text does not specify whether the resistance R of the wire must be kept the same or not: here I assume R must be kept the same.
The relationship between the resistance and the resistivity of a wire is
where
is the resistivity
A is the cross-sectional area
R is the resistance
L is the wire length
the cross-sectional area is given by
where r is the radius of the wire. Substituting in the previous equation ,we find
For the new wire, the length L is kept the same (L'=L) while the radius is doubled (r'=2r), so the new resistivity is
Therefore, the new resistivity must be 4 times the original one.
The relationship between the resistance and the resistivity of a wire is
where
A is the cross-sectional area
R is the resistance
L is the wire length
the cross-sectional area is given by
where r is the radius of the wire. Substituting in the previous equation ,we find
For the new wire, the length L is kept the same (L'=L) while the radius is doubled (r'=2r), so the new resistivity is
Therefore, the new resistivity must be 4 times the original one.
Let us consider two bodies having masses m and m' respectively.
Let they are separated by a distance of r from each other.
As per the Newtons law of gravitation ,the gravitational force between two bodies is given as - where G is the gravitational force constant.
From the above we see that F ∝ mm' and
Let the orbital radius of planet A is = r and mass of planet is
.
Let the mass of central star is m .
Hence the gravitational force for planet A is
For planet B the orbital radius and mass
Hence the gravitational force
Hence the ratio is
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