physics chapter 1 solved exercise | Exercises Physics

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Conceptual Questions For Chapter 1 Measurements

1. For an answer to be complete, the units need to be specified. Why?

Ans: It is meaningless for a number without a unit and a unit does not mean anything without a number

For example :

Let us consider, drawing a line using scale

The measurement given is 5(meaningless)

When there is only only a number, it will lead to a confusion whether to draw a line for cm or m.

Hence, the above mentioned statement is meaningless.

Since the measurement is 5cm. This is making complete sense.

2. What are the advantages of using International System of units (SI)?

Ans: System of units it consists of only 7 days quantity most of the derived quantities are obtained by

multiplying and dividing the base units each quality has only one standard unit should we do not need to

specify the quantity with different units unknown Michael definitions for constant for students to memorize

for example the quantity power is defined as energy per unit time live food is a unit of power is what and it

is defined as the unit of energy per unit time that is Joule per second Si units are inherently derived using the

same equation as quantity decimal exclusively meeting difficult fraction.

3. How many radians accounts for circumference of a circle? How many steradians account for

circumference of a circle?

Ans: Mathematically

Number of radians= 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ

𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒= 𝑆

𝑟

So, the number of revolutions in one radian= 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒

𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑠𝑎𝑚𝑒 𝑐𝑖𝑟𝑐𝑙𝑒 = 2𝜋𝑟

𝑟=2𝜋

Steradians in one Sphere

Mathematically

Number of steradians= 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑒

𝑟2= 4𝜋𝑟2

𝑟2

Number of steradians in sphere= 4𝜋 sr

4: What is the least count error? How can least count error be reduced?

Ans: Least count error

The smallest value that can be measured by the measuring instruments is called its least count.

All the readings or measured values are good only upto this value.

For example a vernier callipers has The least count as 0.01 cm, a spherometer may have a least count of

0.001 cm.

Least count error belongs to the category of random errors but within a limited size, it occurs with both

systematic and random errors.

We can reduce the least count error by using instruments with higher resolution, improving experimental

techniques.

5. Why including more digits in answers, does not make it more accurate?

Ans: Including more digits in answers, does not make it more accurate but it can make answer more precise.

Explanation

Accurate answer is the one which is closest to the actual or acceptable value. For example, actual length of

wire is 10.6 cm. If student A measures its value as 10.5 cm and student B measures it as 10.15 cm. We see

that student A measurement is closer to actual value, so his measurement is more accurate than measurement

of student B, although student B reading has more digits.

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Conceptual Questions For Chapter 1 Measurements

1. For an answer to be complete, the units need to be specified. Why? Ans: It is meaningless for a number without a unit and a unit does not mean anything without a number For example : Let us consider, drawing a line using scale The measurement given is 5(meaningless) When there is only only a number, it will lead to a confusion whether to draw a line for cm or m. Hence, the above mentioned statement is meaningless. Since the measurement is 5cm. This is making complete sense. 2. What are the advantages of using International System of units (SI)? Ans: System of units it consists of only 7 days quantity most of the derived quantities are obtained by multiplying and dividing the base units each quality has only one standard unit should we do not need to specify the quantity with different units unknown Michael definitions for constant for students to memorize for example the quantity power is defined as energy per unit time live food is a unit of power is what and it is defined as the unit of energy per unit time that is Joule per second Si units are inherently derived using the same equation as quantity decimal exclusively meeting difficult fraction. 3. How many radians accounts for circumference of a circle? How many steradians account for circumference of a circle? Ans: Mathematically Number of radians= 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒

𝑆 𝑟 So, the number of revolutions in one radian= 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑠𝑎𝑚𝑒 𝑐𝑖𝑟𝑐𝑙𝑒

2 𝜋𝑟 𝑟

Steradians in one Sphere Mathematically Number of steradians= 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑒 𝑟^2

4 𝜋𝑟^2 𝑟^2 Number of steradians in sphere= 4𝜋 sr 4 : What is the least count error? How can least count error be reduced? Ans: Least count error The smallest value that can be measured by the measuring instruments is called its least count. All the readings or measured values are good only upto this value. For example a vernier callipers has The least count as 0.01 cm, a spherometer may have a least count of 0.001 cm. Least count error belongs to the category of random errors but within a limited size, it occurs with both systematic and random errors. We can reduce the least count error by using instruments with higher resolution, improving experimental techniques.

Why including more digits in answers, does not make it more accurate? Ans: Including more digits in answers, does not make it more accurate but it can make answer more precise. Explanation Accurate answer is the one which is closest to the actual or acceptable value. For example, actual length of wire is 10.6 cm. If student A measures its value as 10.5 cm and student B measures it as 10.15 cm. We see that student A measurement is closer to actual value, so his measurement is more accurate than measurement of student B, although student B reading has more digits.

What determines the precision of a measurement?
If two quantities have different dimensions, is it possible to multiply and/or divide? Can we add and /or subtract them? Ans: No we can add or subtract two terms with same dimensions, but we can multiply or divide two terms with different dimensions. 8.: The human pulse and swing of a pendulum are possible time units. Why are they not often used? Ans: A quantity can be taken as time standard if it is accessible and constant. Human pulse It can not taken as time standard because pulse rate varies as a person rests, walks and runs etc. Swinging Pendulum As the time period can be expressed as But this time period a not serve as a reasonable time standard due to several reasons
Length of pendulum may change due to change in temperature therefore time period may change.
Time period of the simple pendulum varies with G and G varies with altitude.
Frictional force of air and support may effect the time period. 9 : If an equation is dimensionally correct, is that equation a right equation? Ans: If an equation is dimensionally correct, then that equation may or may not be a right equation. For example Consider the equation of Newtons 2nd law F=ma We know that this equation is correct in any sense. But if we write F=2pi MA where 2pi is dimension less constant, so by applying principle of homogeneity, dimensions on L. H. S and R. H. S will be same, therefore it will be dimensionally consistent but it is not correct equation.

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SLS College of Sciences & Arts

Conceptual Questions For Chapter 1 Measurements