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Standard XII

Physics

Relation between Linear and Angular Speed

If ω 1,ω 2,...

Question

If $ω_{1}, ω_{2}, ω_{3}, ω_{4}$ are angular velocities of rotation of earth, seconds hand, minutes hand, hours hand of a watch respectively. Arrange these values in decreasing order.

ω_{1}, ω_{4}, ω_{3}, ω_{2}

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ω_{2}, ω_{3}, ω_{4}, ω_{1}

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ω_{1}, ω_{2}, ω_{3}, ω_{4}

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ω_{4}, ω_{3}, ω_{2}, ω_{1}

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Solution

The correct option is B $ω_{2}, ω_{3}, ω_{4}, ω_{1}$
Time periods of rotation of
earth is 24 hrs
second's hand is 60sec.
minute's hand is 60 min
hour's hand is 12hrs

Now, $ω = \frac{2 π}{T} \Rightarrow ω α \frac{1}{T}$

So, $ω_{1} = \frac{2 π}{86400} = \frac{π}{43200}$
$ω_{2} = \frac{2 π}{60} = \frac{π}{30}$
$ω_{3} = \frac{2 π}{3600} = \frac{π}{1800}$
$ω_{4} = \frac{2 π}{12 \times 3600} = \frac{π}{21600}$

$∴ ω_{2} > ω_{3} > ω_{4} > ω_{1}$

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Similar questions

Q. Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {

{ω_{1}, ω_{2}, ω_{3}, ω_{4}, ω_{5}, ω_{6}, ω_{7}}

Assignment	$ω_{1}$	$ω_{2}$	$ω_{3}$	$ω_{4}$	$ω_{5}$	$ω_{6}$	$ω_{7}$
(a)	0.1	0.01	0.05	0.03	0.01	0.2	0.6
(b)	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$
(c)	0.1	0.2	0.3	0.4	0.5	0.6	0.7
(d)	-0.1	0.2	0.3	0.4	-0.2	0.1	0.3
(e)	$\frac{1}{14}$	$\frac{2}{14}$	$\frac{3}{14}$	$\frac{4}{14}$	$\frac{5}{14}$	$\frac{6}{14}$	$\frac{15}{14}$

If $ω_{1}, ω_{2}$ and $ω_{3}$ represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively in the presence of a gravitational field, then find the correct relation between $ω_{1}, ω_{2}$ and $ω_{3}$ .

Q. If

ω, ω^{2}, ω^{3}, . . . . . . . . ω^{n - 1}

are nth roots of unity then

(1 - ω) (1 - ω^{2}) . . . . . . . (1 - ω^{n - 1})

equals:

Which of the following can not be valid assignment of probabilities for outcomes of sample space S =

Assignment	ω₁	ω₂	ω₃	ω₄	ω₅	ω₆	ω₇
(a)	0.1	0.01	0.05	0.03	0.01	0.2	0.6
(b)
(c)	0.1	0.2	0.3	0.4	0.5	0.6	0.7
(d)	–0.1	0.2	0.3	0.4	–0.2	0.1	0.3
(e)

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If ω1,ω2,ω3,ω4 are angular velocities of rotation of earth, seconds hand, minutes hand, hours hand of a watch respectively. Arrange these values in decreasing order.

The correct option is B ω2,ω3,ω4,ω1Time periods of rotation ofearth is 24 hrssecond's hand is 60sec.minute's hand is 60 minhour's hand is 12hrsNow, ω=2πT⇒ωα1TSo, ω1=2π86400=π43200ω2=2π60=π30ω3=2π3600=π1800ω4=2π12×3600=π21600∴ω2>ω3>ω4>ω1

If $ω_{1}, ω_{2}, ω_{3}, ω_{4}$ are angular velocities of rotation of earth, seconds hand, minutes hand, hours hand of a watch respectively. Arrange these values in decreasing order.