A physical quantity Q is found to depend on observables x, y and z obeying relation Q = (x3y2/z).. The percentage error in the measurements of x, y and z are 1 %, 2 % and 4 % respectively. What is percentage error in the quantity Q ?

Question

A physical quantity Q is found to depend on observables x, y and z obeying relation Q = (x3y2/z).. The percentage error in the measurements of x, y and z are 1 %, 2 % and 4 % respectively. What is percentage error in the quantity Q ? (A) 3% (B) 1% (C) 4% (D) 11%

Tardigrade Admin · Accepted Answer

Q=(x3 y2/z) (given) According to percent error formula (Δ Q/Q) =3|(Δ x/x)|+2|(Δ y/y)|+|(Δ z/z)| where (Δ x/x) =1 %, (Δ y/Y)=2 % and (Δ z/z) =4 %=3 × 1 %+2 × 2 %+1 × 4 % =3 %+4 %+4 %=11 %

Q. A physical quantity Q is found to depend on observables x,y and z obeying relation Q=zx3y2​.. The percentage error in the measurements of x,y and z are 1%,2% and 4% respectively. What is percentage error in the quantity Q ?

3%

1%

4%

11%

Q=zx3y2​ (given) According to percent error formula QΔQ​=3∣∣​xΔx​∣∣​+2∣∣​yΔy​∣∣​+∣∣​zΔz​∣∣​ where xΔx​=1%,YΔy​=2% and zΔz​=4%=3×1%+2×2%+1×4% =3%+4%+4%=11%

Q. A physical quantity $Q$ is found to depend on observables $x, y$ and $z$ obeying relation $Q = \frac{x ^{3} y ^{2}}{z}$ .. The percentage error in the measurements of $x, y$ and $z$ are $1%, 2%$ and $4%$ respectively. What is percentage error in the quantity $Q$ ?