Question

(ii) The length and breadth of a rectangular plate are measured to be (15.30+-0.05)
and (12.80 + -0.05) cm, respectively. The area of the plate and the approximate
uncertainty in the calculated area are (in cm')
(a) 195.8 +0.7% (b) 196.0 +0.7 % (c) 196.0 +0.07% (d) 195.84 +1.4%​

Answer 1

Given : The length and breadth of a rectangular plate are measured to be (15.30 ± 0.05)

and (12.80 ± 0.05) cm, respectively.

To find : The area of the plate and the approximate uncertainty in the calculated area.

solution : Area of rectangular plate , A = l × b

here l = 15. 30 , b = 12.80

so, area of the rectangular plate, A = 15.30 × 12.80

= 195.84 cm² ≈ 195.8

for fractional error, expression is given by,

∆A/A = ∆l/l + ∆b/b

⇒∆A/A = 0.05/15.30 + 0.05/12.80

⇒∆A/A × 100 = (0.05/15.30) × 100) + (0.05/12.80) × 100

⇒percentage error in A = 5/15.30 + 5/12.80

= 0.327 + 0.390

= 0.717 % ≈ 0.7 %

Therefore the area of the plate is given by, (195.8 ± 0.7%). option (a) is correct choice