# Circular Motion Worksheet

Circular Motion Worksheet

Circular motion is the rotation of a body in a circular path or a circular orbit.  When an object is moving in a circular path or a circular orbit it is constantly changing it’s direction.

Here, you can evaluate your knowledge about circular motions by answering the question listed below. The answers to this questions are given on the bottom of the page.

1.  A particular is moving in a circle of radius r with a uniform speed. The angular velocity is

(a)  $\dfrac{v^2}{r}$

(b)  $vr$

(c)  $\dfrac{v}{r}$

(d)  $\dfrac{r}{v}$

2.  A particle is moving along a circular path with uniform speed. Its acceleration is

(a)  Zero

(b)  Directed toward centre

(c)   Directed along the axis of path

(d)   Directed along the tangent at any time

3.  A particular is moving along a circle of radius r with uniform angular speed $\omega$. Then its linear velocity is

(a)  r$\omega$ directed along the axis

(b)  r$\omega$ directed along the radius

(c)   r$\omega$  directed along the tangent

(d)   r$\omega^2$  directed along directed along the radius

4.  A particular is moving along a circular path with uniform speed. Then the angular speed is

(a)  Zero

(b)  Directed along the tangent

(d)  Directed along the axis

5.  A particular is moving in a circle of radius r with a uniform speed. Its centripetal acceleration is

(a)  $\dfrac{v}{r}$ directed towards centre

(b)  $\dfrac{v^2}{r}$ directed towards centre

(c)  $\dfrac{v^2}{r}$ directed away from centre

(d) Zero

6.  Particle is moving in a circle of radius r with a uniform speed. Its angular acceleration is

(a)  $\dfrac{v}{r}$ directed towards center

(b)  $\dfrac{v^2}{r}$  directed towards centre

(c)  $\dfrac{v^2}{r}$  directed along the axis

(d) Zero

7.  At a curved path of the road, the road bed is raised a little on the side away from the centre of the curved path. The slope ($\tan \theta$) of the road bed is given by

(a)  $\dfrac{v^2}{rg}$

(b)  $\dfrac{rg}{v^2}$

(c)  $\dfrac{r}{g v^2}$

(d)  $\dfrac{v^2 g}{r}$

8.  A cyclist turns around a curve at 20km/h. If he turns at the double of this speed, the tendency to overturn is

(a)  Doubled

(b)  Halved

(d)  Unchanged

9.  Railway tracks are banked on curves

(a)  So that no frictional force may be produced between tracks and wheels

(b)  So that the train may not fall down inward

(c)  For providing necessary centripetal force from the horizontal component of normal reaction on the track

(d)  For providing thermal expansion

10.  If a particle moves in a circle, describing equal angles in equal times, its velocity vector

(a)  remains constant

(b)  Change in magnitude only

(c)  Changes in direction only

(d)  Changes both in magnitude and direction

11.  A full circle at the center contains

(a)  $\dfrac{\pi}{4}$ rad

(b)  $\dfrac{\pi}{2}$ rad

(c)  $\pi$ rad

(d)  $2\pi$ rad

12. The angular speed of a second-hand of a watch in radian /sec is

(a) $\dfrac{\pi}{6}$

(b)  $\dfrac{\pi}{30}$

(c)  $\dfrac{\pi}{60}$

(d)  $\dfrac{\pi}{180}$

13.  The angular speed of an hour-band of a watch in radian /min is

(a)  $\dfrac{\pi}{6}$

(b) $\dfrac{\pi}{30}$

(c)  $\dfrac{\pi}{180}$

(d)  $\dfrac{\pi}{360}$

14.  The ratio of angular speed of minute-band and hour-band of a watch is

(a)  1:6

(b)  6:1

(c)  1:12

(d)  12:1

15.  A stone of mass m is tied to a string of length l and rotated in a circle at constant speed v. If the string is released, the stone flies

(c)  Tangentially outward

(d)  With an acceleration $\dfrac{m v^2}{l}$

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

(a)  Constant linear velocity

(b)  Constant acceleration

(c)  Constant force

(d)  Acceleration of constant magnitude with its direction changing

17. A car is travelling with a linear speed v on a circular road of radius R. If it is increasing its speed at the rate of ‘a’ meter/$\sec^2$, then the resultant acceleration will be

(a)  $\dfrac{v^2}{R} - a$

(b)  $\dfrac{v^2}{R} + a$

(c)  $\sqrt{a^2 + \dfrac{v^4}{R^2}}$

(d)  $\sqrt{\left( a^2 + \dfrac{v^2}{R^4}\right)}$

18.  A particle is revolving with a constant speed along a circle path. Keeping its speed constant; its direction of motion is reversed. Then

(a)  The centripetal force does not suffer any change in its direction and magnitude

(b)  The centripetal fore does not suffer any change in magnitude but its direction is reversed

(c)  The centripetal force does not suffer any change in direction, but its magnitude is changed

(d)  The centripetal force becomes 4 times its initial value, without change in its direction

19.  Two particles of equal masses are revolving in circular paths of radii $r_1$  and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

(a)  $\dfrac{r_2}{r_1}$

(b)  $\sqrt{\dfrac{r_2}{r_1}}$

(c)  $\left(\dfrac{r_1}{r_2}\right)^2$

(d)  $\left(\dfrac{r_2}{r_1}\right)^2$

20. Two particles of equal masses are revolving in circular paths of radii $r_1$ and  $r_2$respectively. If they experience centripetal forces, teh ratio of their angular velocities is

(a)  $\dfrac{r_2}{r_1}$

(b)  $\sqrt{\dfrac{r_2}{r_1}}$

(c)  $\left(\dfrac{r_1}{r_2}\right)^2$

(d)  $\left(\dfrac{r_2}{r_1}\right)^2$

21.  Two particles of masses m1 and m2 are revolving in circular paths of radii $r_1$ and $r_2$ respectively with equal angular speeds. Then the ratio of centripetal forces is

(a)  $\dfrac{m_1 r_1}{m_2 r_2}$

(b)  $\dfrac{m_1 r_2}{m_2 r_1}$

(c)  $\sqrt{\dfrac{m_1 r_1}{m_2 r_2}}$

(d)  $\dfrac{m_2}{m_1}\times\dfrac{r_1}{r_2}$

22. Centrifugal force is

(a)  Same as centripetal force

(b)  Gravitational force

(c)  Viscous force

(d)  Apparent force in rotating frame

23.  When an aero plane is looping the loop, the pilot does not fall because his weight

(a)  Acts against gravity

(b)  Provides the centripetal forces

(c)  Is balanced by centrifugal force

(d)  Disappears as g = 0

24.  A cyclist in an Olympic race is moving in a circular track of radius 80 m with speed 72 km/h. He has to learn from the vertical approximately through an angle

(a)  $30^\circ$

(b)   $40^\circ$

(c)   $\tan ^{-1} \left(\dfrac{1}{2} \right)$

(d)   $\tan ^{-1} (2)$

25. A stone tied to the end of a 20 cm long string is whirled in a horizontal circle. If the centripetal acceleration is 9.8 m/  $s^2$, its angular speed is

(a)   $\dfrac{27}{7}$ rad /s

(b)   $7$ rad /s

(c)   $14$ rad /s

(d)   $20$ rad /s

26.  The angular speed of earth’s rotation about its own axis is

(a)  $\dfrac{2\pi}{24 \times 60 \times 60}$ rad /s

(b)  $\dfrac{2 \pi}{365 \times 24 \times 6o \times 60}$ rad /s

(c)   $\dfrac{2\pi}{60 \times 60}$ rad /s

(d)  $\dfrac{2 \pi}{24 \times 60 \times 60}$ rev /s

27.  The angular speed of earth’s revolution about the sun is

(a)   $\dfrac{2 \pi}{24 \times 60 \times 60}$ rad /s

(b)   $\dfrac{2 \pi}{365 \times 24 \times 6o \times 60}$ rad /s

(c)    $\dfrac{2\pi}{365\times 24 \times 60 \times 60}$ rev / s

(d)   $\dfrac{2\pi}{24 \times 60 \times 60}$rev / s

28. For a body moving in a circular path, the condition for no skidding is ($\mu$ = coefficient of friction)

(a)  $\dfrac{m v^2}{r} \ge \mu mg$

(b)  $\dfrac{m v^2}{r}\le \mu mg$

(c)  $\dfrac{m v^2}{r} = \mu$

(d)  $v = \mu gr$

29.  A particle is moving inside a vertical circular frame. It completes the total path if its velocity is greater than $\sqrt{5 rg}$, r being radius of path. If the velocity v is less than $\sqrt{5 rg}$ but greater than $\sqrt{2 rg}$, then

(a)  It will be start oscillating

(b)  It will leave the surface and fall back

(c)  It will leave the inner surface and describe a parabola

(d)  It will slide back after ascending some height

30.  A particle is moving inside a vertical circular frame. It completes the total path, if its velocity of projection is greater than $\sqrt{5 rg}$, r being radius of the path. If its velocity is less than $\sqrt{2 rg}$, then

(a)  It will start oscillating

(b)  It will leave the surface and fall back

(c)  It will slide back after ascending some height

(d)  It will leave the inner surface and describe a parabola

31.  A string is tied to the neck of the bottle full of water containing some air bubbles. If the bottle is revolved in a horizontal circle, the air bubble will

(a)  Remain unaffected

(b)  Be collected at the bottom

(c)  Be collected at the walls of the bottle

(d)  Be collected at the neck

32.  In a circus a rider rides in a circular track of radius r in a vertical plane. The minimum velocity at the highest point of the track will be

(a)   $\sqrt{2 gR}$

(b)  $gR$

(c)   $\sqrt{gR}$

(d)   $\sqrt{3 gR}$

33. Two racing 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 each makes a complete circle in the same length of time t. The ratio of the angular speed of the first to second car is

(a)  $m_1 : r_1$

(b)  $r_1 : r_2$

(c)  1:1

(d)   $m_1 \times r_1 : m_2 \times r_2$

34. Two particles of masses  $m_1$ and  $m_2$ are moving in concentric orbits of radii $r_1$ and $r_2$ such that their periods are same. Then the ratio of their centripetal accelerations is

(a)  $\left(\dfrac{r_1}{r_2}\right)^3$

(b)  $\left( \dfrac{r_2}{r_1}\right) ^3$

(c)  $\dfrac{r_2}{r_1}$

(d)  $\dfrac{r_1}{r_2}$

35.  A particle moves in a circle of radius 30 cm with a constant speed of 6 m/s. Its acceleration is

(a)  Zero

(b)  20 m/$s^2$

(c)  10.8 m/$s^2$

(d)  120 m/$s^2$

36.  A 0.5 kg ball moves in a circle of radius 0.4 m at a velocity of 4 m/s. The centripetal force on the ball is

(a)  10 N

(b)  20 N

(c)  40 N

(d)  80 N

37.  A particle moves in a circle of radius 25 cm at two revolutions/sec. The acceleration of the particle in meter//$sec^2$

(a)  $\pi^2$

(b)  $2\pi^2$

(c)  $4\pi^2$

(d)  $8\pi^2$

38.  A circular platform is rotating about an axis passing through its centre. It completes one revolution in 20 seconds. A girl is sitting on a chair near the edge of the platform. She stands up and walks in a direction opposite to that of the rotation of platform and completes a round to her chair in 10 seconds. The frequency of rotation of the girl relative to ground in revolution /sec is

(a)  $\dfrac{1}{10}$

(b)   $\dfrac{1}{20}$

(c)  10

(d)  Zero

39.  A particle is moving in a circle of radius r centered at O with a constant speed v. The change in velocity in moving from A to B (<AOB= $40\circ$) is

(a)   $2v \cos 40 ^\circ$

(b)  $2v \sin40 ^\circ$

(c)  $2v \cos 20^\circ$

(d)  $2v \sin20 ^\circ$

40.  The length of the second’s-hand of a watch is 1 cm. The change in velocity of its tip in 15 seconds is

(a)  Zero

(b)  $\dfrac{\pi \sqrt{2}}{30} cm/s$

(c)  $\dfrac{\pi}{30\sqrt{2}} cm/s$

(d)  $\dfrac{\pi}{30} cm/s$

41.  What is the ratio of the linear velocities for the points of the minute and hour hands of a clock if the minute hand is 1.5 times longer than the hour hand?

(a)  6

(b)  8

(c)  12

(d)  18

42.  A small disc is placed at the top of a hemisphere of radius R as shown in fig. What is the smallest horizontal velocity that should be given to the disc to the disc for it to leave the hemisphere and not slide down it? Assume no friction.

(a)  $\sqrt{gR}$

(b)  $\sqrt{gR}$

(c)  $2\sqrt{gR}$

(d)  $\sqrt{\dfrac{gR}{2}}$

43.  A car sometimes overturns while taking a turn. When it overturns

(a)  Its inner wheels leave the ground first

(b)  Its outer wheels leave the ground first

(c)  Both the wheels leave the ground simultaneously

(d)  Either wheel leaves the ground first

44.  A train is moving eastwards. At one place it turns north-west. Here we observe that the radius of curvature of the outer rail as compared to that of inner rail will be

(a)  Less

(b)  More

(c)  Equal

(d)  Arbitrary

45.  A small pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits $- \varphi$ and $+ \varphi$. For an angular displacement $\theta$ where $| \theta | < | \varphi |$, the tension T in the string and velocity v of the bob are related as under in the above condition

(a)  $T \cos \theta = Mg$

(b)  $T - Mg \cos \theta = \dfrac{M v^2}{L}$

(c)  $T = Mg \cos \theta$

(d)  Tangential acceleration of bob = $- g \cos \theta$

46.  An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 rpm. The acceleration of a point on the tip of a blade is about

(a)  $1600m/s^2$

(b)  $2370 m/s^2$

(c)  $4740 m/s^2$

(d)  $5055 m/s^2$

47.  Usually an over bridge is convex, the thrust of a vehicle of mass M on the road at the middle position will be

(a)  $Mg + \dfrac{M v^2}{r}$

(b)  $Mg - \dfrac{M v^2}{r}$

(c)  $Mg - \dfrac{v^2}{Mr}$

(d)  $Mg- \dfrac{r}{M v^2}$

48.  If an over bridge is concave instead of convex, the thrust of a vehicle of mass M on the road at the middle position will be

(a)  $Mg + \dfrac{M v^2}{r}$

(b)  $Mg - \dfrac{M v^2}{r}$

(c)  $Mg$

(d)  $\sqrt{\left(Mg\right)^2 + \left(\dfrac{M v^2}{r}\right)^2}$

49.  In washing machine the dustbin is on the wall of the machine, because

(a)  Dust particles are lighter than clothes and they move in a circle of large radius

(b)  Dust particles are heavier than clothes and they are thrown away by centrifugal force

(c)  Dust particles are thrown away by surface tension

(d)  Dust particles are thrown away by viscous forces

50.  A string of a pendulum of mass m and length l is displaced through $90^\circ$ from the vertical and then released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through its mean position is

(a)  mg

(b)  3 mg

(c)  5 mg

(d)  6 mg

51.  A particle of mass m is rotating by means of string in a vertical circle. The difference in the tension at the bottom and the top would be

(a)  0

(b)  2 mg

(c)  4 mg

(d)  6mg

52.  A stone of mass m, is tied to a string. It is whirled in a vertical circle of radius R. Its velocity will be maximum at the position

(a)  A

(b)  B

(c)  C

(d)  D

53.  in Q.52 the tension in the string is maximum at position

(a)   A

(b)  B

(c)  C

(d) D

54.  A 2 kg stone at the end of a string of length 1m is whirled in a vertical circle. It same point its speed is 4 m/s and the tension in the string is 51.6 N. A t this instant the stone is

(a)  At the top of circle

(b)  At the bottom of circle

(c)  Half way down

(d)  At some other position

55. A stone is tied at one end of 2m long string. The minimum speed at the bottom required to complete the circle (in m/s)

(a)  $\sqrt{19.6}$

(b)  $2 \sqrt{9.8}$

(c)  $7 \sqrt{2}$

(d) $7$

56. A person with his hands in his pocket is skating on the ice at the rate of 10m/s and describes a circle of radius 50m. What is his inclination to the vertical ($g = 10m/s^2$).

(a)  $\tan^-1\dfrac{1}{2}$

(b)  $\tan^-1\dfrac{1}{5}$

(c)  $\tan^-1\dfrac{3}{5}$

(d)  $\tan^-1\dfrac{1}{10}$

1. c     2.b     3.c     4.d     5.b

6.d     7.a     8.c     9.c     10.c

11.d     12.b     13.d     14.d        15.c

16.d     17.c     18.a     19.a       20.b

21.a     22.d     23.c     24.c      25.b

16.a     27.b     28.b     29.c     30.a

31.d     32.c     33.c     34.d     35.d

36.b     37.c     38.b     39.d     40.b

41.d     42.b     43.a     44.b     45.b

46.c     47.b     48.a     49.b     50.b

51.d     52.b     53.b     54.b     55.c

56.b

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