Tag: physics

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Questions Related to physics

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

If accuracy of weighing machine is better than 1/2 percent, a student record his own mass. Choose the option that explains the recording most accurately.

  1. 6.43 kg

  2. 60 kg

  3. 64.3 kg

  4. 600kg

  5. 643 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This question is intended to assess your knowledge of realistic values for physical quantities as well as an understanding of experimental error and significant figures. Only 60 kg and 64.3 kg are likely masses for an adult human. When recording measurements, it is assumed that there is some measurement error in the last digit recorded. For both possible values for the student's weight, 1/2 percent is about 0.3 kg. Therefore, a mass recorded to better than this accuracy will indicate tenths of a kilogram.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The length,breadth and thickness of a rectangular copper sheet are $4 cm, 2.5 cm $ and $1.56 cm $ respectively. Find the area of the sheet to corrected significant figures.

  1. $40.3 cm^2$

  2. $40.28 cm^2$

  3. $40 \times 10^2 cm^2$

  4. $0.4\times 10^2 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $l$ be the length, $b$ be the breadth and $t$ be the thickness of the sheet,
then the area of sheet is $A=2(lb+bt+tl)=2[(4\times 2.5)+(2.5\times 1.56)+(1.56\times 4)]=40.28 cm^2$
As length has least significant figures i.e one so the answer must be expressed as one significant figures. 
Thus according rule of determining significant figures, the area will be $0.4\times 10^2 cm^2$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Express 0.006006 into scientific notation in three significant digits:

  1. $6.01 \times 10^{-3}$

  2. $6.0006 \times 10^{-3}$

  3. $6.00 \times 10^{-3}$

  4. $6.0 \times 10^{-3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The number  $0.006006$ has 6 significant figures.
We need to round off the given number to convert into 3 significant figure. Thus,  the correct answer is  $6.01\times 10^{-3}$ as it has 3 significant figure including rounding off.
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Which of the following quantifies has the least number of significant digits? 

  1. $0.80760 $

  2. $0.08765$

  3. $5.7423 \times 10^2$

  4. $80.760$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The number $0.80760$ has $5$ significant digits, $0.08765$ has $4$ significant digits, $5.7423\times 10^{2}$ has $5$ significant digits and $80.760$ has $5$ significant digits.
Hence option B is correct.
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

A person was weighing $102.1\  kg$ last week and gained $0.28 \ kg$ this week. His weight as of now is correctly expressed as :

  1. $102.38\  kg$

  2. $102.3\  kg$

  3. $102.4\  kg$

  4. $102\  kg$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that number of significant figures after addition will be equal to least number of significant figures present in any of the operand.
Therefore total weight after weight gain is $102.1+0.28=102.38 kg$
Now least number of significant figure present after the decimal in the operand is 1, present in $102.1\ kg$ .
Therefore, the number of significant figures present after the calculation should also be $1$ after the decimal. Hence, when we round the answer $102.38$ becomes $102.4\  kg$
Therefore correct answer is option (C)

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Subtract $3.2 \times 10^{-6}$ from $4.7 \times 10^{-4}$ with due regard to significant figures.

  1. $~4.7 \times 10^{-4}$

  2. $~7 \times 10^{-4}$

  3. $~5.7 \times 10^{-4}$

  4. $~4.7 \times 10^{-5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$4.7\times { 10 }^{ -4 }-3.2\times { 10 }^{ -6 }$

$=4.7\times { 10 }^{ -4 }-0.032\times { 10 }^{ -4 }$
$=4.668\times { 10 }^{ -4 }\approx 4.7\times { 10 }^{ -4 }$.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Subtract $1.5 \times 10^3$ from $4.8 \times 10^4$ with due regard to significant figures.

  1. $~4.6 \times 10^{4}$

  2. $~4.6 \times 10^{5}$

  3. $~4.6 \times 10^{6}$

  4. $~5 \times 10^{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$4.8\times { 10 }^{ 4 }-1.5\times { 10 }^{ 3 }$

$=4.8\times { 10 }^{ 4 }-0.15\times { 10 }^{ 4 }$
$\Rightarrow 4.65\times { 10 }^{ 4 }\approx 4.7\times { 10 }^{ 4 }$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Add $3.8 \times 10^{-6} to 4.2 \times 10^{-5}$ with due regard to significant figures.

  1. $~4.6 \times 10^{-5}$

  2. $~4.6 \times 10^{-6}$

  3. $~5.6 \times 10^{-6}$

  4. $~6.6 \times 10^{-5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$3.8\times { 10 }^{ -6 }+42\times { 10 }^{ -6 }=45.8\times { 10 }^{ -6 }=4.58\times { 10 }^{ -5 }$

                                                                      $=4.6\times { 10 }^{ -5 }$.