The dimensional formula for a physical quantity x is [M-1L3T-2]. The errors in measuring the quantities M, L, and T, respectively, are 2 %, 3 %, and 4 %. What is the maximum percentage of error that occurs in measuring the quantity x?

Question

The dimensional formula for a physical quantity x is [M-1L3T-2]. The errors in measuring the quantities M, L, and T, respectively, are 2 %, 3 %, and 4 %. What is the maximum percentage of error that occurs in measuring the quantity x? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

X =M-1 L3 T-2 (Δ X/X) =(Δ M/M) +3 (Δ L/L) +2 (Δ T/T) =2+3× 3+2 × 4=19

Q. The dimensional formula for a physical quantity $x$ is $[M^{- 1} L^{3} T^{- 2}]$ . The errors in measuring the quantities $M, L,$ and $T,$ respectively, are $2%, 3%,$ and $4%$ . What is the maximum percentage of error that occurs in measuring the quantity $x$ ?

$X = M^{- 1} L^{3} T^{- 2}$
$\frac{Δ X}{X} = \frac{Δ M}{M} + 3 \frac{Δ L}{L} + 2 \frac{Δ T}{T}$
$= 2 + 3 \times 3 + 2 \times 4 = 19$

Q. The dimensional formula for a physical quantity x is [M−1L3T−2]. The errors in measuring the quantities M,L, and T, respectively, are 2%,3%, and 4%. What is the maximum percentage of error that occurs in measuring the quantity x?

X=M−1L3T−2 XΔX​=MΔM​+3LΔL​+2TΔT​ =2+3×3+2×4=19

Q. The dimensional formula for a physical quantity $x$ is $[M^{- 1} L^{3} T^{- 2}]$ . The errors in measuring the quantities $M, L,$ and $T,$ respectively, are $2%, 3%,$ and $4%$ . What is the maximum percentage of error that occurs in measuring the quantity $x$ ?

$X = M^{- 1} L^{3} T^{- 2}$
$\frac{Δ X}{X} = \frac{Δ M}{M} + 3 \frac{Δ L}{L} + 2 \frac{Δ T}{T}$
$= 2 + 3 \times 3 + 2 \times 4 = 19$