There is an unknown quantity x=R(l/100 - l) , here l is length (. in cm measured using a scale having least count of 1 cm . and R is a quantity known accurately. Find the percentage error in measurement of x for l = 50 textcm ?

Question

There is an unknown quantity x=R(l/100 - l) , here l is length (. in cm measured using a scale having least count of 1 cm . and R is a quantity known accurately. Find the percentage error in measurement of x for l = 50 textcm ? (A) 1 % (B) 6 % (C) 2 % (D) 4 %

Tardigrade Admin · Accepted Answer

x=R(ℓ /100 - ℓ ) (Δ x/x)=(Δ ℓ /ℓ )+(Δ ℓ /100 - ℓ ) (Δ x/x)× 100=((1/50) + (1/50))× 100=4 %

Q. There is an unknown quantity $x = R \frac{l}{100 - l}$ , here $l$ is length $($ in $c m$ measured using a scale having least count of $1 c m$ . and $R$ is a quantity known accurately. Find the percentage error in measurement of $x$ for $l = 50 cm$ ?

$1 %$

$6 %$

$2 %$

$4 %$

$x = R \frac{ℓ}{100 - ℓ}$
$\frac{Δ x}{x} = \frac{Δ ℓ}{ℓ} + \frac{Δ ℓ}{100 - ℓ}$
$\frac{Δ x}{x} \times 100 = (\frac{1}{50} + \frac{1}{50}) \times 100 = 4%$

Q. There is an unknown quantity x=R100−ll​ , here l is length ( in cm measured using a scale having least count of 1cm . and R is a quantity known accurately. Find the percentage error in measurement of x for l=50cm ?

1%

6%

2%

4%