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The length of vertical alloy pillar structure is dependent on its weight by a specified relation. The relation is directly proportional to the summation of weight and also proportional to the square root of its weight. If the length of vertical alloy pillar was 1320 m and 2880 m, when its weight was 400 kg and 900 kg respectively. Find the exact weight of 7800 m long vertical alloy pillar structure.

The length of vertical alloy pillar structure is dependent on its weight by a specified relation. The relation is directly proportional to the summation of weight and also proportional to the square root of its weight. If the length of vertical alloy pillar was 1320 m and 2880 m, when its weight was 400 kg and 900 kg respectively. Find the exact weight of 7800 m long vertical alloy pillar structure. Correct Answer 2500 kg

Given:

If weight is 400 kg, then length of vertical alloy pillar = 1320 m

If weight is 900kg, then length of vertical alloy pillar = 2880 m

Concept used:

Relation between  length of vertical alloy structure is equal to the summation of weight and square root of its weights.

Calculations:

Let the weight and length of vertical alloy pillar be ‘w’ and ‘l’ respectively.

∵l = x(√w) + y(w)       ----(i)

where x and y are constants.

So,

1320  = x(√400) + y(400)      ----(ii)

2880  = x(√900) + y(900)       ----(iii)

on solving equations (ii) and (iii), we get 

x = 6 and y = 3

For 7800 m long vertical alloy pillar structure,

put values of x and y in equation (i)

⇒ 7800 = 6(√w) +3(w)  

on solving we get value of w = 2500 kg

∴ The exact weight of 7800 m long vertical alloy pillar structure is 2500 kg.

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