JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
A physical quantity \(y\) is represented by the formula \(y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}\). If the percentage error 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 \(4\) and \(\pm 3\)
- B \(5\) and \(\pm 2\)
- C \(8\) and \(\pm 2\)
- D \(\frac{16}{3}\) and \(\pm \frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{16}{3}\) and \(\pm \frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{\Delta y}{y}=\frac{2 \Delta m}{m}+\frac{4 \Delta r}{r}+\frac{x \Delta g}{g}+\frac{3}{2} \frac{\Delta \ell}{\ell}\) \(18=2(1)+4(0.5)+x p+\frac{3}{2}(4)\) \(8=x p\) By checking from options. \(x=\frac{16}{3}, p=\pm \frac{3}{2}\)
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