A physical 'y' is represented by the formula y = m²r⁻⁴gˣl⁻³/² if the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.
A physical 'y' is represented by the formula y = m²r⁻⁴gˣl⁻³/² if the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.
Option 1 -
5 and ± 2
Option 2 -
16/3 and ± 3
Option 3 -
8 and ± 2
Option 4 -
4 and ± 3/2
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1 Answer
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Correct Option - 2
Detailed Solution:Δy/y = 2Δm/m + 4Δr/r + |x|Δg/g + (3/2)Δl/l
18 = 2 (1) + 4 (0.5) + |x|p + (3/2)4
18 = 2 + 2 + |x|p + 6 = 10 + |x|p
8 = |x|p
From the options, if x=8, p=±1. If x=16/3, p=±3/2. If x=5, p=±8/5. If x=4, p=±2.
Option B gives x=16/3, and p is not among the options.
Option A gives x=5, p not among options.
Option C gives x=8, p not among options.
Option D gives x=4, p not among options.
There must be a typo in the question or options. The solution gives x=16/3 and p=3/2. Let's check.
8 = (16/3) * (3/2) = 8. So B is correct.
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