NCERT Class 11 Physics Solutions: Chapter 2-Unit and Measurement Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question: 2.13

A physical quantity P is related to four observables a, b, c and d as follows:

The percentage errors of measurement in a, b, c and d are 1 % , 3 % , 4 % and 2 % respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result?

Answer: 2.13

Image Shows the Definition of Percentage Error

  • Percentage error in P = 13 %
  • Value of P is given as 3.763.
  • By rounding off the given value to the first decimal place, we get

Question: 2.14

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion:

(a)

(b)

(c)

(d)

(a = maximum displacement of the particle,

V = speed of the particle

T = time – period of motion.)

Rule out the wrong formulas on dimensional grounds.

Answer: 2.14

(a)

Answer: correct

  • Dimension of
  • Dimension of
  • Dimension of

  • Hence, the given formula is dimensionally correct.

(b)

Answer: incorrect

  • Dimension of
  • Dimension of
  • Dimension of
  • But the argument of the trigonometric function must be dimensionless, which is not so in the given case. Hence, the given formula is dimensionally incorrect.

(c)

Answer: incorrect

  • Dimension of y =
  • Dimension of
  • Dimension of
  • But the argument of the trigonometric function must be dimensionless, which is not so in the given case. Hence, the formula is dimensionally incorrect.

(d)

Answer: correct

  • Dimension of
  • Dimension of
  • Dimension of
  • Since the argument of the trigonometric function must be dimensionless (which is true in the given case) , the dimensions of y and a are the same. Hence, the given formula is dimensionally correct.

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