Units and Measurements Test

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Units and Measurements Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following represent the number 300,000,000 :

A
$$3 \times 10^6$$

B
$$3 \times 10^7$$

C
$$3 \times 10^8$$

D
$$3 \times 10^9$$

E
$$3 \times 10^{-9}$$

Solution

The given number:
$$300,000,000 =3 \times 10^8$$
Question 2
1 / -0

Students A,B and C measure the diameter of a copper ball using the same screw gauge. A takes 5 readings, B takes 9 readings and C takes 8 readings. The measured value will be most accurate for

A
B

B
A

C
C

D
all

Solution

The accuracy is how close the measured value with the true value. The true value is the average value of the measurements. Thus when more number measurements will be taken, the accuracy will be more. Since student B has taken more readings, so the measured value for B will be most accurate.
Question 3
1 / -0

Which of the following is the smallest unit?

A
millimetre

B
angstrom

C
fermi

D
metre

Solution

Hint:- Convert all units in meter(SI unit) to check the smallest unit.
Explanation:-
$$\bullet$$ Metre is the SI unit of length.
$$\bullet$$ $$1 \ millimetre = 10^{-3} \ metre$$
$$\bullet$$ $$1 \ angstrom = 10^{-10} \ metre$$
$$\bullet$$ $$1 \ fermi = 10^{-15} \ metre$$
So, fermi is the smallest unit.
$$\textbf{Hence option C correct}$$
Question 4
1 / -0

Parallax is the apparent displacement of an object because of:

A
change in observer's point of view

B
change in object's position

C
changes both in observers point of view and object's position

D
consistency in observer's point of view

Solution

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.
As the Earth orbits the sun, a nearby star will appear to move against the more distant background stars. Astronomers can measure a star's position once, and then again 6 months later and calculate the apparent change in position.
Question 5
1 / -0

To minimise parallax error, the observer should place the object :

A
as near to the scale of the ruler as possible and the eye must be directly above the scale

B
as far to the scale of the ruler as possible and the eye must be directly above the scale

C
as near to the scale of the ruler as possible and the eye must be to the right of the scale

D
as near to the scale of the ruler as possible and the eye must be to the left of the scale

Solution

$$Answer:-$$ A
There are three simple ways of reducing parallax error in that case:
1. Attach a straight object (like a ruler or straightened paperclip) to the thing you're measuring the displacement of, it should stick out of the object perpendicularly to the scale you're measuring the displacement on.
2. Make sure that object is as close to your scale as possible, but not touching.
3. Put your eyes level with the object, and as close to it as you safely can.
Question 6
1 / -0

If $$n$$ denotes a positive integer, $$h$$ the Plancks constant, $$q$$ the charge and $$B$$ the magnetic field, then the quantity $$\begin{pmatrix} \dfrac{nh}{2\pi qB}\end{pmatrix}$$ has the dimension of

A
Area

B
Length

C
Speed

D
Acceleration

Solution

Since $$qvB=F$$
$$\implies qB=\dfrac{F}{v}$$
which has dimensions $$[MT^{-1}]$$
$$h$$ has dimensions $$[ML^2T^{-1}]$$
Hence the dimension of $$(\dfrac{nh}{2\pi qB})$$ is $$[L^2]$$, which is that of area.
Question 7
1 / -0

The effect of parallax is used to measure:

A
distances to nearby objects

B
distances to nearby stars

C
nearness of atoms in substances

D
the object and image distance in optical experiments

Solution

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.
As the Earth orbits the sun, a nearby star will appear to move against the more distant background stars. Astronomers can measure a star's position once, and then again 6 months later and calculate the apparent change in position.
Question 8
1 / -0

Which of the following statements regarding dimensions is correct?

A
The dimension of any physical quantity includes the power fundamental physical quantities.

B
Radian is a fundamental physical quantity having dimension.

C
Mutual inductance has no dimension.

D
Dimension of work is same as rate of work done

Solution

Dimensional formula includes power of fundamental quantites.
For example ; Unit of force is [$$M^1L^1T^{-2}$$]
Radian is not a fundamental physical quantity it comes under supplementary units.
Dimension of work is $$[M^1 L^2 T^{-2}]$$ whereas rate of doing work is $$[M^1 L^2 T^{-3}]$$
Question 9
1 / -0

In which of the following pairs, the two physical quantities have different dimensions?

A
Plancks constant and angular momentum

B
Impulse and linear momentum

C
Moment of inertia and moment of a force

D
Energy and torque

Solution

Both plank's constant and angular momentum have dimensions
$$[ML^2T^{-1}]$$
Both impulse and linear momentum have dimensions
$$[MLT^{-1}]$$
Moment of inertia has dimensions
$$[ML^2]$$
Moment of force has dimensions
$$[ML^2T^{-2}]$$
Both energy and torque have dimensions
$$[ML^2T^{-2}]$$
Question 10
1 / -0

Parallax method is based on which of the following principle?

A
Disparity

B
Lutz Kelker bias

C
Trilateration

D
Triangulation

Solution

Distance measurement by parallax is a special case of the principle of triangulation, which states that one can solve for all the sides and angles in a network of triangles if, in addition to all the angles in the network, the length of at least one side has been measured. Thus, the careful measurement of the length of one baseline can fix the scale of an entire triangulation network. In parallax, the triangle is extremely long and narrow, and by measuring both its shortest side (the motion of the observer) and the small top angle (always less than 1 arcsecond leaving the other two close to 90 degrees), the length of the long sides can be determined.

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Units and Measurements Test - 35

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Units and Measurements Test - 35

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Question 1

$$3 \times 10^6$$

$$3 \times 10^7$$

$$3 \times 10^8$$

$$3 \times 10^9$$

$$3 \times 10^{-9}$$

Solution

Question 2

B

A

C

all

Solution

Question 3

millimetre

angstrom

fermi

metre

Solution

Question 4

change in observer's point of view

change in object's position

changes both in observers point of view and object's position

consistency in observer's point of view

Solution

Question 5

as near to the scale of the ruler as possible and the eye must be directly above the scale

as far to the scale of the ruler as possible and the eye must be directly above the scale

as near to the scale of the ruler as possible and the eye must be to the right of the scale

as near to the scale of the ruler as possible and the eye must be to the left of the scale

Solution

Question 6

Area

Length

Speed

Acceleration

Solution

Question 7

distances to nearby objects

distances to nearby stars

nearness of atoms in substances

the object and image distance in optical experiments

Solution

Question 8

The dimension of any physical quantity includes the power fundamental physical quantities.

Radian is a fundamental physical quantity having dimension.

Mutual inductance has no dimension.

Dimension of work is same as rate of work done

Solution

Question 9

Plancks constant and angular momentum

Impulse and linear momentum

Moment of inertia and moment of a force

Energy and torque

Solution

Question 10

Disparity

Lutz Kelker bias

Trilateration

Triangulation

Solution

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