A cylindrical wire of mass (0.4 0.01) g has length (8 0.04) cm and radius (6 0.03) cm. The maximum error in its density will be [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A cylindrical wire of mass (0.4 $\pm$ 0.01) g has length (8 $\pm$ 0.04) cm and radius (6 $\pm$ 0.03) cm. The maximum error in its density will be [2023]

1 1%

2 4%

3 5%

4 3.5%

Ans.
(2)

$ρ = \frac{m}{π r^{2} l} \Rightarrow$ $| \frac{d ρ}{ρ} |_{\max}$ $=$ $| \frac{d m}{m} |$ $+ 2$ $| \frac{d r}{r} |$ $+$ $| \frac{d l}{l} |$

$= \frac{0.01}{0.4} + \frac{2 (0.03)}{6} + \frac{0.04}{8}$

$\Rightarrow % error in density = (\frac{d ρ}{ρ}) \times 100 %$

$= (2.5 + 1 + 0.5) % = 4 %$

Want Us to Email you About Special Offers & Updates?