Physical World Units And Measurements Ques 44
44. The percentage errors in the measurement of mass and speed are $2 \%$ and $3 \%$ respectively. The error in kinetic energy obtained by measuring mass and speed will be
[1995]
(a) $12 \%$
(b) $10 \%$
(c) $8 \%$
(d) $2 \%$
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Answer:
Correct Answer: 44.(c)
Solution:
- (c) Percentage error in mass $(\frac{\Delta m}{m} \times 100)=2$
and percentage error in speed $(\frac{\Delta v}{v} \times 100)=3$.
Kinetic energy, $k=\frac{1}{2} m v^{2}$.
$\therefore$ Error in measurement of kinetic energy $\frac{\Delta K}{K}=\frac{\Delta m}{m}+2(\frac{\Delta v}{v})$
$=(\frac{2}{100})+(2 \times \frac{3}{100})=\frac{8}{100}=8 \%$
$\therefore \%$ age error $=8 \%$.
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