Question

A rectangular metal slab of mass 33.333g has its length 8cm, breadth 5cm and thickness 1mm.The mass is measured with accuracy up to 1mg with a sensitive balance.The length and breadth are measured with vernier callipers having a least count of 0.01cm.The thickness is measured with a screw gauge of least count 0.01mm.The percentage accuracy in density calculated from the above measurement is

Answer 1

Dear Student,

Density of rectangular slab is calculated as: $\frac{Mass}{Volume}=\frac{M}{2\left(lb+bh+hl\right)}$
Thus,
$$\begin{gathered} \frac{\Delta \rho }{\rho }=\frac{\Delta M}{M}+2\left(\frac{\Delta l}{l}+\frac{\Delta b}{b}+\frac{\Delta h}{h}\right) \\ \Rightarrow \frac{\Delta \rho }{\rho }=\left(\frac{0.1}{33.333}+2\left(\frac{\Delta 0.01}{8}+\frac{\Delta 0.01}{5}+\frac{\Delta 0.01}{1}\right)\right)\times 100=2.95\% \end{gathered}$$
Regards