Units and Measurements Test

Result

Units and Measurements Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72” of arc. Calculate the diameter of Jupiter.

A
1.632×10⁵km

B
1.429×10⁵km

C
1.523×10⁵km

D
1.321×10⁵km

Solution

Distance of Jupiter from the Earth, D = 824.7 × 10⁶ km

Angular diameter = 35.72“ = 35.72 × 4.874 × 10^-6 rad

Diameter of Jupiter = d

Using the relation, θ = d/D

d = θ× D = 824.7 × 10⁶ × 35.72 × 4.872 × 10^-6≅1.429×10⁵km
Question 2
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A man walking briskly in rain with speed v must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v : tan θ = v and checks that the relation has a correct limit: as v→0,θ→0, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Which of the following is correct?

A
derivation is wrong; correct formula is tan θ = v/v’ where v’ is speed of rain

B
derivation is correct; correct formula is tan θ = v

C
derivation is wrong; correct formula is cos θ = v/v’ where v’ is speed of rain

D
derivation is wrong; correct formula is sin θ = v/v’ where v’ is speed of rain

Solution

Incorrect;

Dimension of R.H.S = M⁰ L¹T^-1

Dimensionof L.H.S = M⁰ L⁰ T⁰

(The trigonometric function is considered to be a dimensionless quantity) Dimension of R.H.S is not equal to the dimension of L.H.S.

Hence, the given relation is not correct dimensionally. To make the given relation correct, the R.H.S should also be dimensionless.

One way to achieve this is by dividing the R.H.S by the speed of rainfall. Therefore, the relation reduces to tanθ = v/v

This relation is dimensionally correct.
Question 3
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Horse power is unit of

A
Time

B
Distance

C
Power

D
Current

Solution

The horsepower (hp) is a unit in the foot-pound-second ( fps ) or English system, sometimes used to express the rate at which mechanical energy is expended. It was originally defined as 550 foot-pounds per second (ft-lb/s). A power level of 1 hp is approximately equivalent to 746 watt.
Question 4
1 / -0

The significant digits in 0.000532 are

A
0,5,3,2

B
2, 3

C
5, 3, 2

D
5, 3
Solution
There are three rules on determining how many significant figures are in a number:
- Non-zero digits are always significant.
- Any zeros between two significant digits are significant.
- A final zero or trailing zeros in the decimal portion ONLY are significant.
Keeping these rules in mind, we can say that only 5,3,2 are significant digits.