Units and Measurements - Online Test

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q1. If θ is the parallax angle of a planet at a distance 'D', when observed from two different positions on the Earth, separated by distance 'b', the expression for 'D' is

A. θb

\frac{b}{θ}

C. 2bθ

D. θ2b

Answer : Option B
Explaination / Solution:

Parallax Method of Measurement : Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view.

To measure the distance D of a far away planet S by the parallax method, We observe it from two different positions (observatories) A and B on the Earth, separated by distance AB=b at the same time as shown in the given figure.

We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in the figure represented by symbol θ is called the parallax angle or parallactic angle.

As the planet is very far away, bD<<1 and therefore, θ is very small. Then we approximately take AB as an arc of length b of a circle with center at S and the distance D as the radius AS=BS so that AB=b=Dθ where θ is in radians.

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q2. Absolute error of the measurement is

A. the difference between two individual measurements and their mean

B. the difference between the individual measurement and the true value of the quantity

C. the difference between the individual measurement and the true value of the quantity cubed.

D. the difference between the individual measurement and the true value of the quantity squared.

Answer : Option B
Explaination / Solution:

Absolute error is defined as the magnitude of difference between the actual and the individual values of any quantity in question.

Say we measure any given quantity for n number of times and a1 , aa2 , aa3 ….. an are the individual values then Arithmetic mean

am =( [a1+a2+a3+ ….. + an]/n )

Now absolute error formula as per definition

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q3. The arithmetic mean of all the absolute errors

Δ a_{m e a n}

is given by

A.
Δamean=(|Δa1|+|Δa2|+|Δa3|+...+|Δan|)

B. Δamean=2(|Δa1|+|Δa2|+|Δa3|+...+|Δan|)n

C. Δamean=(|Δa1|+|Δa2|+|Δa3|+...+|Δan|)n

D. 2Δamean=(|Δa1|+|Δa2|+|Δa3|+...+|Δan|)n

Answer : Option C
Explaination / Solution:

Mean is the average of all numbers. So mean of all the absolute errors will be given by $\frac{s u m o f a l l a b s o l u t e e r r o r s}{n u m b e r o f e r r o r s}$

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q4. The relative error is given by

A. Relative error=Δamean2amean

R e l a t i v e e r r o r = Δ a m e a n a m e a n

C. Relative error=2Δameanamean

D. Relative error=Δamean1.2amean

Answer : Option B
Explaination / Solution:

Relative Error or fractional error : It is defined as the ration of mean absolute error to the mean value of the measured quantity.

$δ a = \frac{m e a n a b s o l u t e v a l u e}{m e a n v a l u e}$

$R e l a t i v e e r r o r (δ a) = \frac{Δ a_{m e a n}}{a_{m e a n}}$

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q5. Percentage error δa is given by

δ a = (Δ a_{m e a n} / a_{m e a n})

%

δ a = (Δ a_{m e a n} / a_{m e a n})

200

%

δ a = (Δ a_{m e a n} / a_{m e a n})

%

δ a = (Δ a_{m e a n} / a_{m e a n})

100

%

Answer : Option D
Explaination / Solution:

Percentage Error: It is the relative error measured in percentage.

So Percentage Error $δ a = \frac{m e a n a b s o l u t e v a l u e}{m e a n v a l u e} \times 100$

$δ a = \frac{Δ a_{m e a n}}{a_{m e a n}} \times 100$ %

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q6. When two quantities are added or subtracted, the absolute error in the final result is

A. absolute value of the sum of individual quantities

B. absolute value of the difference of errors of individual quantities

C. the sum of the absolute errors in the individual quantities

D. absolute value of the sum of errors of individual quantities

Answer : Option C
Explaination / Solution:

When two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities.

e.g: error $∆ x$ in the sum x=a+b is $∆ x = \pm (∆ a + ∆ b)$

maximum value of error $∆ x$ = $(∆ a + ∆ b)$

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q7. When two quantities are multiplied or divided, the relative error in the result is

A. the sum of the relative errors in the multipliers

B. the difference of the absolute errors in the multipliers

C. the sum of the absolute errors in the multipliers

D. the difference of the relative errors in the multipliers

Answer : Option A
Explaination / Solution:

When two quantities are multiplied or divided, the relative error in the result is the sum of the relative errors in the multipliers.

e.g x=a x b

maximum possible error is: $\frac{∆ x}{x} = \pm (\frac{∆ a}{a} + \frac{∆ b}{b})$

similarly, for error in quotient: x= $\frac{a}{b}$

maximum possible error is: $\frac{∆ x}{x} = \pm (\frac{∆ a}{a} + \frac{∆ b}{b})$

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q8. The relative error in a physical quantity raised to the power k is.

A. k times the relative error in the individual quantity

B. k times the absolute error in the individual quantity

C. (k – 1) times the relative error in the individual quantity

D. (k – 1) times the absolute error in the individual quantity

Answer : Option A
Explaination / Solution:

The relative error in a physical quantity raised to a power k is the k times the relative error in the individual quantity.

for e.g. $x = \frac{a^{n}}{b^{m}}$

maximun relative error, $\frac{∆ x}{x} = \pm (n \frac{∆ a}{a} + m \frac{∆ b}{b})$

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q9. The significant figures of a number

A. are those digits that carry meaning contributing to its accuracy

B. are those that are at odd positions after decimal

C. are those that are at even positions after decimal

D. are all non zero digits

Answer : Option A
Explaination / Solution:

The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:

All leading zeros;
Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures); and
Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.

# Units and Measurements # CBSE 11TH PHYSICS Prepare / Learn

Q10. According to the principle of homogeneity of dimensions

A. we can add similar physical quantities

B. we can add or subtract any physical quantities

C. we can add or subtract similar physical quantities

D. we can subtract similar physical quantities

Answer : Option C
Explaination / Solution:

It would be more exact to say that "Quantities with the same units can be added and subtracted with no problem." Quantities with the same dimensions can often be added and subtracted as long as the units are correctly converted.

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