Motion In A Plane - Important Concept For NEET

Q 1 :
A particle moving with uniform speed in a circular path maintains [2024]

constant velocity
constant acceleration
constant velocity but varying acceleration
varying velocity and varying acceleration

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4

(4)

In uniform circular motion velocity does not remain constant as direction of motion keeps changing. Hence, velocity varies continuously and thus, acceleration also changes.

Q 2 :
Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

$1 : 1$
$r_{A} : r_{B}$
$v_{A} : v_{B}$
$r_{B} : r_{A}$

1

2

3

4

(1)

Time period, $T = \frac{2 π}{ω}$

As $T_{A} = T_{B} .$ So, $\frac{2 π}{ω_{A}} = \frac{2 π}{ω_{B}}$ or $ω_{A} : ω_{B} = 1 : 1$

Q 3 :
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

$\frac{V_{0}}{n} {rad/s}^{2}$
$\frac{V_{0}}{2 π n r^{2}} {rad/s}^{2}$
$\frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$
$\frac{V_{0}^{2}}{4 π n r} {rad/s}^{2}$

1

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(3)

Distance travelled in $n^{th}$ rounds $= (2 π r) n$

Using $v^{2} = u^{2} + 2 a s$ or, $V_{0}^{2} = 0 + 2 a (2 π r) n \Rightarrow a = \frac{V_{0}^{2}}{4 π n r}$

Angular acceleration, $α = \frac{a}{r} = \frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

Q 4 :
In the given figure, $a = 15 {ms}^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 m$ at a given instant of time. The speed of the particle is [2016]

[IMAGE 13]

$4.5 {ms}^{- 1}$
$5.0 {ms}^{- 1}$
$5.7 {ms}^{- 1}$
$6.2 {ms}^{- 1}$

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(3)

[IMAGE 14]----------------------------------

Here, $a = 15 {ms}^{- 2}, R = 2.5 m$

From Figure, $a_{c} = a \cos 30 ° = 15 \times \frac{\sqrt{3}}{2} {ms}^{- 2}$

As we know, $a_{c} = \frac{v^{2}}{R} \Rightarrow v = \sqrt{a_{c} R}$

$∴ v = \sqrt{15 \times \frac{\sqrt{3}}{2} \times 2.5} = 5.69 ≃ 5.7 {ms}^{- 1}$

Topic Question Set

Q 1 :
A particle moving with uniform speed in a circular path maintains [2024]

Q 2 :
Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

Q 3 :
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

Q 4 :
In the given figure, $a = 15 {ms}^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 m$ at a given instant of time. The speed of the particle is [2016]

[IMAGE 13]

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Topic Question Set

Q 1 : A particle moving with uniform speed in a circular path maintains [2024]

Q 2 : Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed vA and vB respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

Q 3 : A particle starting from rest, moves in a circle of radius 'r'. It attains a velocity of V0 m/s in the nth round. Its angular acceleration will be [2019]

Q 4 : In the given figure, a=15ms-2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5m at a given instant of time. The speed of the particle is [2016] [IMAGE 13]

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Q 1 :
A particle moving with uniform speed in a circular path maintains [2024]

Q 2 :
Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

Q 3 :
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

Q 4 :
In the given figure, $a = 15 {ms}^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5 m$ at a given instant of time. The speed of the particle is [2016]

[IMAGE 13]