KPK 11th Class Physics Chapter 1 Measurement Short Questions Answers

A number (π):

The circumference of a circle divided by the diameter of the some circle is known as number (π).

  π=circumference/diometer of circle

Generally, it is taken as 227 i.e. π=22/7 

To show that, a π radion = 360°

Radion is the angle subtended at the centre of a circle by an ore equal in length to its radios. 

Now, if Are length = r, then =1 radion and if Are length = (2 π)r , then θ=2π radion. Here ‘2 πr’ represents the length of circular path thus in one circle or in one revolution we have 2 π radion. i.e. 

Revolution = 2 π radion ………………(1)

We also know that, “Degree” is the angle subtended at the centre of a circle by 1/360th part of its circumference. Thus there are 360° in one circle (or) on one revolution. i.e. 

1 revolution = 360° ……………………………………..(2)

Comparing eq (1) and eq (2) we get,

   2 radion = 360°

1) Error: The difference between value of a quantity is known as error.

2) Uncertainty: An estimate of the possible range of an error is known as uncertainty.

  Or

The error which arises due to nat-yral imperfections of the experimenter, the limitation of the apparatus and the changes in the environment during the measurement is known as uncertainty.

 3) Precision: The measure of the consistency of measurement is known as precision. It represent the magnitude of error in a measurement.

4) Accuracy: “The measure of correctness of a measurement is known as accuracy.” 

The accuracy means to check how the measure values is closer to the actual value. It is a relation error. It  o an be obtained by dividing the error with measured quantity. The accuracy depends on the error. If the error is greater, then smaller will be the accuracy of the measurement and vice versa. The accuracy of the measurement o an be increased by taking several readings and then take their average.

“Any phenomenon that repeats itself after regular time intervals can be used as a time standard.”

The several repetitive phenomenon occurring naturally which could served reasonable time standards are given below.

1. The motion of earth around the sun and its spin motion can be used as reasonable time standards.
2. Revolution of moon around the earth can be used as reasonable time standards.
3.   Characteristic vibration of crystals such as quartz crystal can be used as reasonable time standards.
4. Some other repetitive phenomena which can be adopted to define a time standards are heart beat, human pulse rate, radio-active decay rate of some substances, changing of seasons, change of shadow of an object in the sun light etc.

We find it useful to have two units for the amount of substance i.e. kilogram and mole. It is because, in case of large quantity or solids or liquids, we can do measurement in a unit like kilogram easily. While in case of gases or vapour, we can do means urement in a unit like mole easily. For example, water (liquids), ice (solids), vapours (gas) represents the three states of matter. In case of ice and water, we can use “kilogram” as a measuring unit. While in case of gas or vapours, we can use “mole” as a measuring unit.

  E = mc2

Taking L.H.S,

Let E = mgh = [M] [L/T²][L] 

•  E = [M] [L²][T^-2] => E = [ML²T^-2] ………(2)

Now taking R.H.S of eq (1) , we get,

 mc2 =M [L/T]²  =[ ML²T^-2]

• mc² = [ML²T^-2]…………………………(3)

Comparing eq (2) and eq (3) we see that ‘E’ and ‘mc2’ have same dimensions. So the Einstein equation i.e. E = mc2 is dimensionally consistent or dimensionally correct.

From Newton’s law of gravitation, we have, 

  F = G m, m₂/r²

• G = Fr²/m₁m₂   …………………..(1)

Here F = ma = M.L/T²=[MLT^-2]

• F = [MLT^-2]  ………………. (2)

And  r² = [L²] = [L²]

• r²= [L²]…………. (3)

And m1m2=MM[M2]

• m₁m₂= [M²]……………………..(4) 

Putting eqs (2) ,(3), (4) in eq (1), we get,

G = [MLT^-2][L²]/[M²]

• G = [M^-1L³T^-2]

We know that, 

K.E = ½mv²

=> K.E = kg (m/sec⁡)²

=> K.E = kg m²/ sec² ……………………………(1)

Now replacing the units by their corresponding dimensions, we get,

 K.E = [ML²/T²]     =   [ML²T^-2]

=> K.E =  [ML²T^-2]

We know that the time period of a simple pendulum is given by 

T= 2π √e/g ………………..(1)

Eq (1) shows that the period of a simple pendulum depends upon the length ‘l’ of the string and value of ‘g’.

Now in hot or cold seasons, the length ‘l’ may be effected due to expansion or contraction respectively.

Similarly, we know that the value of ‘g’ varies with altitude and depth.

Due to variation in values of ‘l’ and ‘g’ the time period of simple pendulum will be effected. 

Due to such drawback, we cannot use the period of simple pendulum as a time standard.

Radians and steradians are not the basic units of SI. These are the units of purely geometrical quantities i.e. plane angle and solid angle respectively. The General conference on weight and measures has not yet classified these units under either base units or derived units. These are called supplementary units.

‘Micro’ means very small. Microwaves have the shortest wavelengths of all the radio waves, therefore, these are known as micro waves.

Now like all electromagnetic waves, the microwaves produces heating effect when their energy is absorbed. It is because, due to shorter wave length, the micro waves posses high frequency and maximum energy.

The water will absorb microwaves of one particular frequency. This principle is used in microwave ovens, where micro waves penetrate deep into food and heat up the water in it.

The density of air is given by, S = 1.2 kg /m³ ………………..(1)

We know that,

     1 Kg = 1000 gm

1 m = 100 cm

And 

So eq (1) becomes,

S = 1.2 ×1000 gm/(100cm)³

• S = 1.2 ×1000gm/(100×100×100) cm3
• S = 1.2× 10³/10⁶cm³          = 1.2 ×10^3-6 gm / mc³
• S = 1.2 ×10^-3 gm/cm³

The analogous statement is that, “the result of an experimental date which is as accurate as measurement are be used in the computation.”

 Or

“the accuracy of the final result cannot be greater than the least accurate measurement.”

For example, let the length and width of a rectangular surface is 3.251 m and 1.6m respectively. We can find the area of this rectangular surface as under;

Area = Length x width 

• A = 3.251 m × 1.6m
• A = 5.2016 m²

Now in given data, we see that “width’’ has least significant figures, so we round off the final measurement [i.e. A = 5.2016 m²]  to two significant figures. i.e. 

  A = 5.2 m²

1) Light Year:

Light year is the unit of distance. It is defined as, “the distance travelled by light in vacuum in one year.”

1 light year = 9.46 10¹⁵m  

1. ii) Year: Year is the unit of time. Interval in which the earth completes one revolution around the sun.”

1 year = 365.25 days.

And 

1 year = 365.25 ×24×3600 sec

• 1 year = 31557600 sec