A physical quantity 'y' is represented by the formula y = m² r⁻⁴ gx… | JEE Main 2021 (27 Jul, Shift 2)

Q80JEE Main 2021 · 27 JUL · SHIFT 2Medium

Errors in Measurement

A physical quantity 'y' is represented by the formula $y = m^{2} r^{-4} g^{x} l^{-\frac{3}{2}}$

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.

Show answer and solution

Answer: (c)

$y = m^2 r^{-4} g^x l^{-3/2} \Rightarrow \frac{\Delta y}{y} = 2\frac{\Delta m}{m} + 4\frac{\Delta r}{r} + x\frac{\Delta g}{g} + \frac{3}{2}\frac{\Delta l}{l}$
$18 = 2(1) + 4(0.5) + xp + \frac{3}{2}(4) = 10 + xp$
So $xp = 8$ . Check options: $\frac{16}{3} \times \frac{3}{2} = 8$ ; others give 10, 12, 16.
So the answer is (c) $\frac{16}{3}$ and $\pm\frac{3}{2}$ .

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