Circular Motion

Q1

Let $ω_{1}, ω_{2}$ and $ω_{3}$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_{1}, x_{2}$ and $x_{3}$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is :

[Re-NEET 2024]

a

$\frac{ω_{1}}{x_{1}} = \frac{ω_{2}}{x_{2}} = \frac{ω_{3}}{x_{3}} = k$

b

$ω_{1} x_{1} = ω_{2} x_{2} = ω_{3} x_{3} = k$

c

$ω_{1} x_{1}^{2} = ω_{2} x_{2}^{2} = ω_{3} x_{3}^{2} = k$

d

$ω_{1}^{2} x_{1} = ω_{2}^{2} x_{2} = ω_{3}^{2} x_{3} = k$

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Q2

Let $ω_{1}, ω_{2}$ and $ω_{3}$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_{1}, x_{2}$ and $x_{3}$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is :

a

$\frac{ω_{1}}{x_{1}} = \frac{ω_{2}}{x_{2}} = \frac{ω_{3}}{x_{3}} = k$

b

$ω_{1} x_{1} = ω_{2} x_{2} = ω_{3} x_{3} = k$

c

$ω_{1} x_{1}^{2} = ω_{2} x_{2}^{2} = ω_{3} x_{3}^{2} = k$

d

$ω_{1}^{2} x_{1} = ω_{2}^{2} x_{2} = ω_{3}^{2} x_{3} = k$

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Q3

A particle moving with uniform speed in a circular path maintains :

a

constant velocity.

b

constant acceleration.

c

constant velocity but varying acceleration.

d

varying velocity and varying acceleration.

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Q4

A bob is whirled in a horizontal plane by means of a string with an initial speed of $ω r p m$ . The tension in the string is T. If speed becomes $2 ω$ while keeping the same radius, the tension in the string becomes:

a

T

b

4T

c

$\frac{T}{4}$

d

$\sqrt{2} T$

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Q5

Let $ω_{1}, ω_{2}$ and $ω_{3}$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_{1}, x_{2}$ and $x_{3}$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is :

[Re-NEET 2024]

a

$\frac{ω_{1}}{x_{1}} = \frac{ω_{2}}{x_{2}} = \frac{ω_{3}}{x_{3}} = k$

b

$ω_{1} x_{1} = ω_{2} x_{2} = ω_{3} x_{3} = k$

c

$ω_{1} x_{1}^{2} = ω_{2} x_{2}^{2} = ω_{3} x_{3}^{2} = k$

d

$ω_{1}^{2} x_{1} = ω_{2}^{2} x_{2} = ω_{3}^{2} x_{3} = k$

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Q6

Let $ω_{1}, ω_{2}$ and $ω_{3}$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_{1}, x_{2}$ and $x_{3}$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is :

[Re-NEET 2024]

a

$\frac{ω_{1}}{x_{1}} = \frac{ω_{2}}{x_{2}} = \frac{ω_{3}}{x_{3}} = k$

b

$ω_{1} x_{1} = ω_{2} x_{2} = ω_{3} x_{3} = k$

c

$ω_{1} x_{1}^{2} = ω_{2} x_{2}^{2} = ω_{3} x_{3}^{2} = k$

d

$ω_{1}^{2} x_{1} = ω_{2}^{2} x_{2} = ω_{3}^{2} x_{3} = k$

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Q7

Let $ω_{1}, ω_{2}$ and $ω_{3}$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_{1}, x_{2}$ and $x_{3}$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is :

[Re-NEET 2024]

a

$\frac{ω_{1}}{x_{1}} = \frac{ω_{2}}{x_{2}} = \frac{ω_{3}}{x_{3}} = k$

b

$ω_{1} x_{1} = ω_{2} x_{2} = ω_{3} x_{3} = k$

c

$ω_{1} x_{1}^{2} = ω_{2} x_{2}^{2} = ω_{3} x_{3}^{2} = k$

d

$ω_{1}^{2} x_{1} = ω_{2}^{2} x_{2} = ω_{3}^{2} x_{3} = k$

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