Question

The percentage error in measuring M, L and T are $1\%,1.5\%$ and $3\%$ respectively. Then the percentage error in measuring the physical quantity with dimensions $\left[M{L}^{-1}{T}^{-1}\right]$ is

• A. $1\%$
• B. $3.5\%$
• C. $3\%$
• D. $4.5\%$
• E. $5.5\%$

Answer 1

The correct option is E $5.5\%$

Given, percentage error in measuring M = $1\%$
Percentage error in measuring $L=1.5\%$
Percentage error in measuring $T=3\%$
Now the percentage error in measuring the physical quantity with dimenstion $\left[M{L}^{-1}{T}^{-1}\right]$ is
$\frac{△x}{x}\times 100=\frac{△M}{M}\times 100+\frac{△L}{L}\times 100+\frac{△T}{T}\times 100$
$\frac{△x}{x}\times 100=1+1.5+3$
$\frac{△x}{x}\times 100=5.5\%$