Tag: motion and measurement

Questions Related to motion and measurement

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

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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. $9.66 cm$

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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. $0.2 cm$

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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

A star is $1.45\ parsec$ light years away. How much parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?

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

  1. $2\ Parsec$

  2. $0.725\ Parsec$

  3. $1.45\ Parsec$

  4. $2.9\ Parsec$

Show answer
Correct Option: A
Explanation:

One light year $=$ speed of light $\times$ one year

or $1 ly=3\times 10^8\times (24\times 3600)=94608\times 10^{11} m$
So, $4.29 ly=4.29\times (94608\times 10^{11})=4.058\times 10^{16} m$
As $1 $ parsec $=3.08\times 10^{16} m$
(Parsec is a unit of length used to measure large distances to objects outside our Solar System)
Thus, $4.29 ly=\dfrac{4.058\times 10^{16}}{3.08\times 10^{16}}=1.32$ parsec
Now angular displacement , $\theta=\dfrac{d}{D}$
where $d=$ diameter of earth's orbit $= 3\times 10^{11} m$ and 
$D=$ distance of star from the earth $=4.058\times 10^{16} m$
So, $\theta=\dfrac{3\times 10^{11}}{4.058\times 10^{16}}=7.39\times 10^{-6}$ rad
As $1 sec=4.85\times 10^{-6} rad$ so, $7.39\times 10^{-6} rad=\dfrac{7.39\times 10^{-6}}{4.85\times 10^{-6}}=1.52 sec$

Metre is the SI unit of

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. mass

  2. volume

  3. length

  4. area

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Correct Option: C
Explanation:

Metre is the SI unit of length.

Pressure is a standard unit of time.

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. True

  2. False

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Correct Option: B
Explanation:

Second is a standard unit of time. Thus the given statement is false.

Quantity of matter contained in a body is ....................... .

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. Mass

  2. density

  3. relative density

  4. Volume

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Correct Option: A
Explanation:

Mass of the body is defined as the quantity of matter contained in a body.

Knot is a measure of:

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. The speed of ship

  2. The curvature of spherical objects

  3. Solar radiation

  4. Intensity of earthquake shock.

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Correct Option: A
Explanation:

Knot is a measure of the speed of ship. The term knot dates from the 17th century, when sailors measured the speed of their ship by using a device called a "common log".

Hence, option A is correct.

Which one of the following does not have unit of force per unit area:

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $Stress$

  2. $Strain$

  3. $Youngs Modulus$

  4. $pressure$

Show answer
Correct Option: B
Explanation:
  • Stress  is the force per unit area on a body that tries to cause a change in shape. It is measured by the SI unit is Pascal.

  • Strain is defined as the deformation produced in a solid due to stress. It is measured by calculating the ratio of the two lengths. As a result it does not have any unit.  

  • Force is measured by the product of mass and acceleration. Its SI unit is Newton.

  • Pressure is measured by force per unit area. Its SI unit is Pascal.

So correct answer is option (B).