Uniform Circular Motion

Q. A tachometer is a device to measure

1. Gravitational pull
2. Speed of rotation
3. Surface tension
4. Tension in a spring

Q. A particle moves along a straight line such that its velocity (v) at any time (t) is given by v = (2t – 1) m/s, where t is in seconds. Total distance travelled by the particle in first second is

एक कण किसी सरल रेखा के अनुदिश इस प्रकार गति करता है कि किसी समय (t) पर इसके वेग (v) को v = (2t – 1) m/s द्वारा व्यक्त किया जाता है, जहाँ t सेकण्ड में है। प्रथम सेकण्ड में कण द्वारा तय की गई कुल दूरी है

1. $\frac{3}{8}$ m
2. $\frac{1}{2}$ m
3. $\frac{1}{4}$ m
4. Zero
   
   (शून्य)

Q. Two cars $c_1$ and $c_2$ are going around in concentric circles of radii $r_1$ and $r_2$. They complete the circular paths in the same time. Then, the ratio of speed of $c_1$ to speed of $c_2$ is

1. $\frac{r_2}{r_1}$
2. $\frac{r_1}{r_2}$
3. $1$
4. None of these

Q. A hemi spherical bowl of radius ${}^{\prime }R=0.1{\text{m}}^{\prime }$ is rotating about its own axis (which is vertical) with an angular velocity ${}^{\prime }{\omega }^{\prime }$ . A particle of mass ${}^{\prime }{10}^{-2}{\text{kg}}^{\prime }$ is also rotating with same ${}^{\prime }{\omega }^{\prime }$ on the friction-less inner surface of the bowl. The particle is at a height ${}^{\prime }{h}^{\prime }$ from the bottom of the bowl.



The relation between ${}^{\prime }{h}^{\prime }$ and ${}^{\prime }{\omega }^{\prime }$ is

1. $h=\frac{{\omega }^2}{g}$
2. $h=\frac{R}{2}$
3. $h=R-\frac{g}{{\omega }^2}$
4. None

Q.

A car moves on a circular path of radius 10 metre. It complete 5 revolution in 5 minute. What is its average speed?

1. 10 $\pi$ m / minute

2. 20 $\pi$ m / minute

3. 30 $\pi$ m / minute

4. 5 $\pi$ m / minute

Q. A particle initially at rest, moves along x-axis, such that its acceleration varies with time t as a = (4t + 5) m/s². If it starts from origin, then distance travelled by particle in 2 second will be

एक कण प्रारम्भ में विराम में है, यह x-अक्ष के अनुदिश इस प्रकार गति करता है कि इसका त्वरण, समय t के साथ a = (4t + 5) m/s² के अनुसार परिवर्तित हो। यदि यह मूल बिन्दु से गति प्रारम्भ करता है, तब 2 सेकण्ड में कण द्वारा तय की गई दूरी होगी

1. $\frac{23}{4}m$
2. $\frac{49}{3}m$
3. $\frac{46}{3}m$
4. $\frac{51}{7}m$

Q.

A motor cyclist going round in a circular track at constant speed has

1. Constant linear velocity

2. Constant acceleration

3. Constant angular velocity

4. Constant force

Q.

An object is moving in a circle of radius 100 m with a constant speed of 31.4 m/s. What is its average speed for one complete revolution

1. $Zero$

2. $31.4m/s$

3. $3.14m/s$

4. $\sqrt{2}\times 31.4m/s$

Q. A body is moving in a circular path with a constant speed if it has

1. a constant velocity.
2. a constant acceleration
3. an acceleration of constant magnitude.
4. an acceleration which varies with time in magnitude.

Q.

A particle is moving along a circular path of radius $0.7\mathrm{m}$ with tangential acceleration of $5{\mathrm{ms}}^{-2}$ The particle is initially at rest.
Based on above information, answer the following question:

3.The distance travelled by the particle in $7\text{s}$ is

1. $123\mathrm{m}$

2. $725\mathrm{m}$

3. $728\mathrm{m}$

4. $426\mathrm{m}$

Q. A body is undergoing uniform circular motion. The dot product of its acceleration and velocity is

1. positive
2. negative
3. zero
4. either positive or zero

Q.

The average acceleration vector for a particle having a uniform circular motion is

1. A constant vector of magnitude $\frac{v^2}{r}$

2. A vector of magnitude $\frac{v^2}{r}$directed normal to the plane of the given uniform circular motion

3. Equal to the instantaneous acceleration vector at the start of the motion

4. A null vector

Q. Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane in circular path with ‘O’ as center. If the velocity of the outermost particle is $v_0$, then the ratio of tensions in the three sections of the string is

1. 3 : 5 : 7
2. 3 : 4 : 5
3. 7 : 11 : 6
4. 3 : 5 : 6

Q. A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\text{sec}$ it rotates through an angle ${\theta }_1$, in the next $2\text{sec}$ it rotates through an additional angle ${\theta }_2$. The ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

1. $1$
2. $2$
3. $3$
4. $5$

Q. Velocity and acceleration vectors of a charged particle moving in a magnetic field at some instant are $\overrightarrow{v}=3\hat{i}+4\hat{j}$ and $\overrightarrow{a}=2\hat{i}+x\hat{j}$ (Select the correct alternative(s).

1. $x=-1.5$
2. $x=3$
3. Magnetic field is along z - direction.
4. Kinetic energy of the particle is constant

Q. A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completes half of the circular path?

1. ${360}^{\circ }$
2. ${180}^{\circ }$
3. ${45}^{\circ }$
4. $0^{\circ }$

Q. Two particles are moving in different circles in same plane with different angular velocities as shown in figure. At $t=0$, initial positions of particles $A$ and $B$ are shown by dots on the respective circles. Initial distance between particles is $1\text{m}$. Particle $A$ move anticlockwise in the first circle whereas $B$ moves clockwise in the second circle. Angle described (rotated) by $A$ and $B$ in time $t$ are ${\theta }_A=\left(\frac{\pi }{2}t\right)$ and ${\theta }_B=\left(\pi t\right)$ respectively. Here $\theta$ is in radian and $t$ is in second. Radius of each circle is shown in diagram. At time $t=2\text{sec}$, the angular velocity of the particle $A$ with respect to the particle $B$ is

1. $\frac{5\pi }{6}$ rad/s
2. $\frac{3\pi }{2}$ rad/s
3. $\frac{\pi }{3}$ rad/s
4. $\frac{\pi }{2}$rad/s

Q. The coordinates of a particle at any time t is given by x = 4t – 3t² and y = 3t. Equation of trajectory followed by particle is

किसी समय t पर एक कण के निर्देशांकों को x = 4t – 3t² तथा y = 3t द्वारा व्यक्त किया जाता है। कण द्वारा अनुसरित प्रक्षेप-पथ की समीकरण है

1. 3x = 4y – 3y²
2. 3x = y – 4y²
3. 3x = 4y – y²
4. x = 3y – 4y²

Q. A particle is moving in a horizontal circle with constant speed. It has constant

1. Velocity
2. Acceleration
3. Kinetic energy
4. Displacement

Q. A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel?

1. 0.25 cm
2. 2 cm
3. 4 cm
4. 2.5 cm

Q. In a situation shown below, if the speed of the tip of the seconds hand is $v\text{m/s}$, find the magnitude of change in its velocity.

1. $1.732v\text{m/s}$
2. $1.414v\text{m/s}$
3. $0.707v\text{m/s}$
4. $v\text{m/s}$

Q. A car is moving on a circular path with a constant speed of $10m/s$. What is the magnitude of change in velocity when it moves through ${120}^{\circ }$?

1. $0$
2. $10\sqrt{3}m/s$
3. $10m/s$
4. $10\sqrt{2}m/s$

Q. A fly wheel of mass $140\text{kg}$ and radius $3\text{m}$ is rotating at $240\text{rpm}$. The angular acceleration of flywheel if it comes to rest, after $7$ rotations is (Assume constant angular acceleration)

1. $\frac{16}{7}\pi \frac{rad}{s^2}$
2. $\frac{-16}{7}\pi \frac{rad}{s^2}$
3. $\frac{8\pi }{7}\frac{rad}{s^2}$
4. $\frac{-8\pi }{7}\frac{rad}{s^2}$

Q.

Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 km/s. Then,

1. The average velocity of the earth from 1st Jan, 90 to 30th June, 90 is zero

2. The average acceleration during the above period is 60 km/s²

3. The average speed from 1st Jan, 90 to 31st Dec, 90 is zero

4. The instantaneous acceleration of the earth points towards the sun.

Q.

A particle is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point

1. The momentum changes by mv

2. The momentum changes by 2mv

3. The kinetic energy changes by $\left(\frac{1}{2}\right)m{v}^2$

4. The kinetic energy changes by $m{v}^2$

Q. When a ceiling fan is switched off, its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest? (Assume uniform angular retardation)

1. 12
2. 18
3. 24
4. 54

Q. Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane in circular path with ‘O’ as center. If the velocity of the outermost particle is $v_0$, then the ratio of tensions in the three sections of the string is

1. 3 : 5 : 7
2. 3 : 4 : 5
3. 7 : 11 : 6
4. 3 : 5 : 6

Q. The $x$ and $y$ coordinates of a particle are $x=A\sin \left(\omega t\right)$ and $y=A\sin (\omega t+\frac{\pi }{2})$. The motion of the particle is ($x$ and $y$ are in the directions shown in the figure)

1. circular clockwise
2. circular anti-clockwise
3. elliptical
4. rectilinear

Q. A particle is moving along a circular path with a constant speed of $10\text{m/s}$. Find the magnitude of change in velocity of the particle when it moves through an angle of ${60}^{\circ }$ around the centre of the circle.

1. $10\sqrt{2}\text{m/s}$
2. $10\text{m/s}$
3. $10\sqrt{3}\text{m/s}$
4. $\text{Zero}$

Q. A person is standing at a latitude which makes an angle of ${60}^{\circ }$ with the centre of earth. What is the % change in his actual weight here. Take reference of weight near earth's pole as actual weight. Take $g=10{\text{m/s}}^2$.

1. $8$%
2. $0.08$%
3. $0.008$%
4. $0.0008$%