Practice portal › Units and Measurements › Errors in Products, Quotients and Powers

A physical quantity y is represented by the formula y=m²r⁻⁴g^xl^-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

Asked in JEE Main 27th July 2nd Shift 2021 · Percentage error in a derived quantity

Answer: (4) (16)/3 and ±3/2

Step-by-step solution

Idea: every exponent weights its own percentage error, in magnitude.

(Δ y)/y=2(Δ m)/m+4(Δ r)/r+x(Δ g)/g+3/2(Δ l)/l

18=2(1)+4(0.5)+xp+3/2(4)

18=2+2+xp+6, so xp=8.

Of the four pairs only (16)/3×3/2=8 satisfies this.

Why the other options are wrong

More Errors in Products, Quotients and Powers questionsAll Errors in Products, Quotients and Powers questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer