Question

A rectangular metal slab of mass $33.333g$ has its length 8.0 cm, breadth 5.0 cm and thickness 1mm. The mass is measured with accuracy up to 1 mg with a sensitive balance. The length and breadth are measured with vernier calipers having the least count of 0.01 cm. The thickness is measured with a screw gauge of least count 0.01mm. The percentage accuracy in density calculated from the above measurements is :

• A. $13$%
• B. $130$%
• C. $1.32$%
• D. $16$%

Answer 1

The correct option is C $1.32$%

Volume of the slab is $V=lbt$

Density $\rho =\frac{Mass}{Volume}=\frac{m}{V}=\frac{m}{lbt}$

So, $\frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+\frac{\Delta l}{l}+\frac{\Delta b}{b}+\frac{\Delta t}{t}=\frac{{10}^{-3}}{33.333}+\frac{0.01}{8}+\frac{0.01}{5}+\frac{0.01}{1}=0.0132$

Thus, percentage error in density $=\frac{\Delta \rho }{\rho }\times 100=0.0132\times 100=1.3\%$