JEE Advanced2018PhysicsMathematics in PhysicsActual
Paragraph: If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x y . If the errors in x , y a n d z a r e ∆ x , ∆ y a n d ∆ z , respectively, then z ± ∆ z =
Options
- A∆ a 1 + a 2
- B2 ∆ a 1 + a 2
- C2 ∆ a 1 - a 2
- D2 a ∆ a 1 - a 2
Correct answer
B. 2 ∆ a 1 + a 2
Step-by-step solution
r = 1 - a 1 + a ∆ r r = ∆ 1 - a   1 - a + ∆ 1 + a 1 + a =   ∆ a 1 - a + ∆ a 1 + a =   ∆ a 1 + a + 1 - a 1 - a 1 + a ∴       ∆ r = 2 ∆ a 1 - a 1 + a 1 - a 1 + a = 2 ∆ a 1 + a 2