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

Solution:

If L is the length of the aluminium rod and,

Mass of the rod is M

Then M ∝ L

M = kL

where k is a positive proportionality constant

k = M/L

k = 192/16

k = 12

If the mass of the rod M = 105g then the length of the rod is:

M = kL

k = 12

M = 12L

105 = 12L

L = 105/12

L = 35/4

L = 8.75m

✦ Try This: The mass of an aluminium rod varies directly with its length. If a 12 cm long rod has a mass of 144 g, find the length of the rod whose mass is 216 g.

If L is the length of the aluminium rod and,

Mass of the rod is M

Then M ∝ L

M = kL

where k is a positive proportionality constant

k = M/L

k = 144/12

k = 12

If the mass of the rod M = 216g then the length of the rod is:

M = kL

k = 12

M = 12L

216 = 12L

L = 216/12

L = 18

L = 18 m

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 73

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

Summary:

The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, the length of the rod whose mass is 105 g is 8.75m

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