A) 0.9%
B) 2.4%
C) 3.1%
D) 4.2%
Correct Answer: C
Solution :
[c] : Least count of screw gauge \[=\frac{\text{pitch}}{\text{no}\text{.}\,\text{of}\,\text{divisions}\,\text{on}\,\text{circular}\,\text{scale}}\] \[=\frac{0.5}{50}=0.01mm.\] Diameter of ball, \[D=MSR+CSR\times LC\] \[=2.5mm+20\times 0.01mm=2.7mm\] As density, \[\rho =\frac{\text{mass}}{\text{volume}}=\frac{M}{\frac{4\pi }{3}{{\left( \frac{D}{2} \right)}^{3}}}\] Relative error in the density,\[\frac{\Delta \rho }{\rho }=\frac{\Delta M}{M}+\frac{3\Delta D}{D}\] Relative percentage error in the density is \[\frac{\Delta \rho }{\rho }\times 100=\left( \frac{\Delta M}{M}+\frac{3\Delta D}{D} \right)\times 100\] \[\frac{\Delta M}{M}\times 100+\frac{3\Delta M}{D}\times 100=2+3\times \frac{0.01}{2.7}\times 100\] \[=2%+1.11%=3.1%\]You need to login to perform this action.
You will be redirected in
3 sec