Tag: measurement of small and large distances

Questions Related to measurement of small and large distances

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

physics motion and measurement measuring length measurement of small and large distances measurement of distance

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

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

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

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

Show answer
Correct Option: A
Explanation:

$Answer:-$ 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.

The effect of parallax is used to measure:

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. distances to nearby objects

  2. distances to nearby stars

  3. nearness of atoms in substances

  4. the object and image distance in optical experiments

Show answer
Correct Option: B
Explanation:

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.

A star has a parallax angle p of 0.723 arcseconds. What is the distance of the star?

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. 1.38 parsecs

  2. 2.38 parsecs

  3. 3.38 parsecs

  4. 4.38 parsecs

Show answer
Correct Option: A
Explanation:

Relationship between a star's distance and its parallax angle:

$d=\dfrac{1}{p}$

The distance $d$ is measured in parsecs and the parallax angle $p$ is measured in arcseconds.

Hence, $d=\dfrac{1}{0.723}=1.38 parsecs$

Error due to eye vision is termed as :

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. climax error

  2. sight error

  3. parallax error

  4. visional error

Show answer
Correct Option: C
Explanation:

$Answer:-$ C

Parallax also affects optical instruments such as rifle scopes, binoculars,microscope and twin lens reflex cameras that view objects from slightly different angles. Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis.

A star's distance ($d$) and its parallax angle ($p$) are related to each other as:

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $d=\dfrac{1}{p}$

  2. $d=\dfrac{1}{p^2}$

  3. $p=\dfrac{1}{d^2}$

  4. none of these

Show answer
Correct Option: A
Explanation:

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.

The relationship between a star's distance and its parallax angle:

$d=\dfrac{1}{p}$

The distance $d$ is measured in parsecs and the parallax angle $p$ is measured in arc seconds.

Parallax method is based on which of the following principle?

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. Disparity

  2. Lutz Kelker bias

  3. Trilateration

  4. Triangulation

Show answer
Correct Option: D
Explanation:

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.

Parallax angles _______ $0.01/ arcsec$ are very difficult to measure from Earth.

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. more than

  2. less than

  3. equal to

  4. greater than or equal to

Show answer
Correct Option: B
Explanation:

Parallax effect depends upon the path of light that travels from object to the observer. For distant objects observed from Earth, the light that reaches Earth has to go through a number of layers in Earth's atmosphere, during which it refracts and disperses and hence decreases the accuracy of the method. Resultantly parallax angles less than $0.01/arcsec$ are very difficult to measure from Earth.

A student measure the height h of a convex mirror using spherometer. The legs of the spherometer are 4 cm apart and there are 10 divisions per cm on its linear scale and circular scale has 50 divisions. The student takes 2 as linear scale division and 40 as circular scale division. What is the radius of curvature of the convex mirror ?   

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $9.06 cm$

  2. $20.66 cm$

  3. $5.66 cm$

  4. $9.66 cm$

Show answer
Correct Option: D
Explanation:

Least count of the spherometer is $LC=$ pitch/number of circular divisions $=\dfrac{1/10}{50}=0.002 cm$
The total reading for height is $h=MSR+(CSR\times LC)=(2\times 0.1)+(40\times 0.002)=0.28 cm$
The formula for radius of curvature is $R=\dfrac{l^2}{6h}+\dfrac{h}{2}=\dfrac{4^2}{6(0.28)}+\dfrac{0.28}{2}=9.66 cm$

A spherometer has 10 threads per cm and its circular scale has 50 divisions. The least count of the instrument is  

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $0.01 cm$

  2. $0.02 cm$

  3. $0.002 cm$

  4. $0.2 cm$

Show answer
Correct Option: C
Explanation:

The least count of the spherometer, $LC=$pitch/ total number of circular divisions $=\dfrac{p}{n}$
Here, pitch $p=1/20=0.1\ cm$ and $n=50$
Thus, $LC=\dfrac{0.1}{50}=0.002\ cm$

If a star is $5.2\times 10^{16}\ m$ away. What is the parallax angle in degrees?

physics motion and measurement measuring length measurement of small and large distances measurement of distance

  1. $1.67 \times 10^{-4}$ degrees

  2. $1.67 \times 10^{-5}$ degrees

  3. $0.67 \times 10^{-4}$ degrees

  4. $2.3 \times 10^{-4}$ degrees

Show answer
Correct Option: A
Explanation:

Given :    $1$ AU $ = 1.5\times 10^11$ m                $d = 5.2\times 10^{15}$ m

Parallax angle:     $\alpha = \dfrac{1 AU}{d} =\dfrac{1.5\times 10^{11}}{5.2\times 10^{16}} = 0.288\times 10^{-5}$  radians
$\implies$   $\alpha = \dfrac{180}{\pi} \times 0.288\times 10^{-5} = 1.67\times 10^{-4}$  degrees