The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, then find the length of the rod whose mass is 105 g.

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8.75 cm

8.00 cm

8.50 cm

8.25 cm

answer is A.

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Detailed Solution

Given the mass of an aluminium rod varies directly with its length and a 16 cm long rod has a mass of 192 g.
We need to find the length of the rod whose mass is 105 g.
Assume that length of the rod whose mass is 105 g is

l

cm.
Use the given fact that mass of an aluminum rod varies directly with its length hence ratio of mass and length would be constant.

\frac{mass}{length} = constant

Equate the ratio of 192 g mass and 16 cm length with ratio of 105 g with

l

cm to solve, for

l

\frac{105}{l} = \frac{192}{16}

\frac{105 \times 16}{192} = l

\frac{105}{12} = l

\frac{35}{4} = l

\Rightarrow l = 8.75

Length of the rod whose mass is 105 g is 8.75 cm.
Hence, the correct option is 1.

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