Kinematics of Circular Motion

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A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^{3} + 5$ , where $s$ is in metre and $t$ is in second. The radius of the path is $20 m$ . The acceleration of $P$ when $t = 2 s$ is nearly

13 ms^{- 2}

(B)

12 ms^{- 2}

(C)

7.2 ms^{- 2}

(D)

14 ms^{- 2}

LEVELJEE Main

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

(A)

The velocity vector is tangent to the circle

(B)

The acceleration vector is tangent to the circle

(C)

The acceleration vector points to the centre of the circle

(D)

The velocity and acceleration vectors are perpendicular to each other

JEE Main 2020

LEVELJEE Main

A particle moves such that its position vector $r (t) = cos ω t \hat{i} + sin ω t \hat{j}$ , where $ω$ is a constant and $t$ is time. Then, which of the following statements is true for the velocity $v (t)$ and acceleration $a (t)$ of the particle?

(A)

v

and

a

both are parallel to

r

(B)

v

is perpendicular to

r

and

a

is directed away from the origin.

(C)

v

and

a

both are perpendicular to

r

(D)

v

is perpendicular to

r

and

a

is directed towards the origin.

LEVELJEE Main

For a particle in uniform circular motion the acceleration $a$ at a point $P (R, θ)$ on the circle of radius $R$ is (here, $θ$ is measured from the $x$ -axis)

(A)

- \frac{v ^{2}}{R} cos θ \hat{i} + \frac{v ^{2}}{R} sin θ \hat{j}

(B)

- \frac{v ^{2}}{R} sin θ \hat{i} + \frac{v ^{2}}{R} cos θ \hat{j}

(C)

- \frac{v ^{2}}{R} cos θ \hat{i} - \frac{v ^{2}}{R} sin θ \hat{j}

(D)

\frac{v ^{2}}{R} \hat{i} + \frac{v ^{2}}{R} \hat{j}

JEE Main 2020, 6 Sep Shift-I

LEVELJEE Main

A clock has a continuously moving second's hand of $0.1 m$ length. The average acceleration of the tip of the hand (in $ms^{- 2}$ ) is of the order of

(A)

1 0^{- 3}

(B)

1 0^{- 4}

(C)

1 0^{- 2}

(D)

1 0^{- 1}

JEE Main 2021, 27 Aug Shift-I

LEVELJEE Advanced

A huge circular arc of length $4.4 ly$ subtends an angle $4 s$ at the centre of the circle. How long it would take for a body to complete $4 rev$ if its speed is $8 AU per sec$ ? [Given, $1 ly = 9.46 \times 1 0^{15} m, 1 AU = 1.5 \times 1 0^{11} m$ ]

(A)

4.1 \times 1 0^{8} s

(B)

4.5 \times 1 0^{10} s

(C)

3.5 \times 1 0^{6} s

(D)

7.2 \times 1 0^{8} s

LEVELJEE Main

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ , respectively. Their speeds are such that they make complete circles in the same time $t$ . The ratio of their centripetal acceleration is

(A)

m_{1} r_{1} : m_{2} r_{2}

(B)

m_{1} : m_{2}

(C)

r_{1} : r_{2}

(D)

1 : 1

JEE Main 2019, 12 Jan Shift-II

LEVELJEE Main

Two particles $A$ and $B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $ω$ . At $t = 0$ , their positions and direction of motion are shown in the figure. The relative velocity $v_{A} - v_{B}$ at $t = \frac{π}{2 ω}$ is given by

(A)

ω (R_{1} + R_{2}) \hat{i}

(B)

- ω (R_{1} + R_{2}) \hat{i}

(C)

ω (R_{1} - R_{2}) \hat{i}

(D)

ω (R_{2} - R_{1}) \hat{i}

JEE Main 2019, 11 Jan Shift-I

LEVELJEE Main

A particle is moving along a circular path with a constant speed of $10 ms^{- 1}$ . What is the magnitude of the change in velocity of the particle, when it moves through an angle of $6 0^{\circ}$ around the centre of the circle?

(A)

102 m/s

(B)

10 m/s

(C)

103 m/s

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $ω$ . The discs are in the same horizontal plane. At time $t = 0$ , the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_{r}$ . In one time period ( $T$ ) of rotation of the discs, $v_{r}$ as a function of time is best represented by Note: Language of the question is wrong. Magnitude of relative velocity should be asked.

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $a$ is correctly shown in

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Starting from the centre of a circular path of radius $R$ , a particle P chases another particle Q that is moving with a uniform speed $v$ on the circular path. The chaser P moves with a constant speed $u$ and always remains collinear with the centre and the location of the chased Q. (a) On which path will P eventually move and how long will it take to reach on this path? Consider the cases $u < v$ , $u = v$ and $u > v$ . (b) If speeds of the particles are $v = 4 m/s$ and $u = 8 m/s$ and radius of the circular path is $R = 84 m$ , how long P will take to reach Q. Use $π = 22/7$ .

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A boy starts from point A and passes point C of a track ABC shown in the figure. Portion AB of length $l$ is straight and portion BC is a semicircle of radius $r$ ( $r < l$ ). Anywhere on the track, the modulus of the maximum acceleration of the boy is $a$ . Find minimum transit time of the boy from A to C.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Two students simultaneously start from the same place on a circular track and run for 2 min. In this time, one of them completes three and the other four revolutions. Due to thick vegetation in a circular area as shown in the figure, either of the boys can see only one third of the track at a time. How long during their run do they remain visible to each other?

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

A straight track is tangent to a circular track of radius $r$ . Two material points A and B start simultaneously from the common point of the tracks. The point A moves with uniform velocity $u$ on the straight track whereas the point B on the circular track always keeping itself collinear with the centre of the circular track and the point A. Find suitable expression for magnitude of acceleration of the point B when it is at angular position $θ$ .

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

One end of a light inextensible thread of length $l$ is held stationary over a frictionless horizontal floor while a small bead tied at the other end of the thread is describing a circular path with a uniform speed $v_{0}$ on the floor as shown in the figure. The upper end of the thread is suddenly pulled vertically upwards with a constant acceleration $a_{0}$ . If the bead does not leave the floor, find magnitude of its acceleration immediately after the upper end of the thread is pulled.

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Particle A moves with a constant speed $2 m/s$ on a circular path of radius $4 m$ whereas particle B moves along a straight line through the centre of the circular path always maintaining a constant distance $4 m$ from the particle A. Which of the following conclusions can be drawn?

* Multiple Correct Options

(A)

Maximum speed of B is

4 m/s

(B)

Maximum acceleration of B is

2 m/s^{2}

(C)

During one revolution of A, distance travelled by B is

32 m

(D)

Modulus of velocity of a particle relative to the other is a constant.

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a particle in uniform circular motion the acceleration a at a point P(R,θ) on the circle of radius R is (here, θ is measured from the x-axis)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in ms−2) is of the order of

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a is correctly shown in

For a particle in uniform circular motion the acceleration $a$ at a point $P (R, θ)$ on the circle of radius $R$ is (here, $θ$ is measured from the $x$ -axis)

A clock has a continuously moving second's hand of $0.1 m$ length. The average acceleration of the tip of the hand (in $ms^{- 2}$ ) is of the order of

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $a$ is correctly shown in