Q. The relative density of the material of a body I the ratio of its weight in air and the loss of its weight in water. By using a spring balance, the weight of the body in air in measured to be 5.00 $\pm 0.05$N. The weight of the body in water is measured to be $4.00 \pm 0.05$N. Then the maximum possible percentage error in relative density is
A) 11%
B) 10%
C) 9%
D) 7%
Explanation
RD$= \frac{w_{1}}{w_{1} - w_{2}},\frac{\mathrm{\Delta}(RD)}{RD} \times 100$ $= \frac{\mathrm{\Delta}w_{1}}{w_{1}} \times 100 + \frac{D(w_{1} - w_{2})}{w_{1} - w_{2}} \times 100$ $= \frac{0.05}{5.00} \times 100 + \frac{0.05 + 0.05}{1.00} \times 100 = 1 + 10 = 11\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.