Circular Motion Questions and Answers

No 39 View In English one hand and the free end of the string by the other hand The mass is sot into revolution in a A small stone of mass m is attached to a light string which passes through a hollow tube The tube is held b horizontal circle of radius ry with a speed v The string is pulled down shortening the radius of the circular path to r2 Which of the following is not correct w Ex have usual meanings T is tension 1 2 3 4 w2 Wy Exi Ex Ex Ex s

A stone tied to the end of a string of 1m long is whirled in a horizontal circle with a constant speed If the stone makes 22 revolution in 44 seconds what is the magnitude and direction of acceleration of the stone 1 7 m s and direction along the tangent to the circle 2 m s and direction along the radius towards the centre 3 m s and direction along the radius towards 4 the centre 4 7 m s and direction along the radius away from the centre

Two particles having mass M and m are moving in a circular path having radius R and r If their time period are same then the ratio of angular velocity will be 1 r B R 2 3 1 4 R

13 A small bead of mass m is stationary with respect to rotating ring of radius R Angular speed of ring about a vertical diameter AA is and distance of mass m from the line AA is r Then find the value of speed of bead 1 ro 3 ro AK 2 RO

A stone is tied to one end of string 50 cm long and is whirled in a horizontal circle with constant speed If the stone makes 10 revolutions in 20 s then what is the magnitude of acceleration of the stone 1 493 cm s 3 860 cm s 2 720 cm s 4 990 cm s

A particle moving along a circular path The angular velocity linear velocity angular acceleration and centripetal acceleration of the particle at any instant respectively are o v a a Which of the following relation is are correct a o I v 1 a b d 10 10 b I a 2 b c d c vlac 3 a b c d olac 4 a c d

SolveLancer Test The disc of radius R is confined to roll without slipping If the plates have the velocities as shown in the figure then find the magnitude of difference in acceleration of points A and B V b 8v R c 0 d 4v B 3v SolveLancer Test

The figure shows the velocity vo and acceleration a of a point like body at the initial moment of its motion The acceleration vector of the body remains constant The minimum radius of curvature in trajectory of the body in metre is a 4 m s 8 150 16 m s

2 24 A solid sphere rolls on a rough horizontal surface with a linear speed 7 m s collides elastically with a fixed smooth vertical wall Then the speed of the sphere when it has started pure rolling in the backward direction is m s

A particle of mass m and carrying charge q is moving around a charge q2 along a circular path of radius r Find period of revolution of the charge 91 1 0 3 16 mr 9192 9192 2 8n mr 9192

A point P moves in counter clockwise direction on a circular path as shown in the igure The movement of P is such that it sweeps out a length s t 5 where s s in metres and t is in seconds The radius of the path is 16 m The acceleration of P when t 2 s is nearly mark answer in m s y B 16 m P x y A X

A ball is projected with horizontal velocity v 9gR at the bottom most point attached with inextensible string of length R fixed at O as shown Tension in the string in horizontal position is kmg the value of k is

A rigid rod of length and negligible mass has a ball of mass m attached to one end with its other end fixed to form a pendulum as shown in figure The pendulum is inverted with the rod vertically up and then released Find the speed of the ball and the tension in the rod at the lowest point of the trajectory of ball l

A satellite revolves in the equatorial plane around the earth at an altitude equal to radius of the earth A very sensitive device can detect its shadow made on the earth surface by the sunrays Find average velocity of the shadow relative to a non rotating frame fixed with the centre of the earth Escape velocity from the earth surface is u

nt of maximum friction What stored in the he top of a g is fired elocity of led in it 4 8 A ball of mass m is shot with a velocity u at an angle 0 with the horizontal which strikes the box of mass M resting at the edge of a smooth table as shown in figure 4 129 After striking the box ball falls down vertically Find the value of u such that the box is raised to the point A shown in figure Also find the horizontal distance from which shot was fired Ans f m u 0 M 2gR M Figure 4 129 2 M R tan 0 R

Consider the rectangular section below where h is greater than b X Y h b Which of the following statements are true Moment of inertia about the x axis is greater than the moment of inertia about the y axis ly Moment of inertia about the y axis ly is greater than the moment of inertia about the x axis I Radius of gyration about the x axis k is greater than the radius of gyration about the y axis ky Radius of gyration about the y axis ky is greater than the radius of gyration about the x axis k As a column subjected to compressive loading the section will tend to buckle about the x axis As a column subjected to compressive loading the section will tend to buckle about the y axis

The sinusoidal potential difference V shown in figure applied across a resistor R produces heat at a rate W What is the rate of heat dissipation when the square wave potential difference V as shown in figure is applied across the resistor V V Vo 1 W 2 V Vol 2 W 4 2W

3 A hemispherical bowl is placed on a frictionless horizontal floor and small disc is placed on the top of the bowl as shown in the figure Th disc and the bowl are of equal mass and there is no friction betwee them The disc is slightly pushed horizontally so that it starts slidin down the bowl with a negligible speed At what angular displacement the disc measured from a vertical line through the centre of the bow will the disc lose contact with the bowl

During the motion of a planet around the sun which the following physical quantity remains conserved 1 Moment of inertia of planet about sun 2 Angular velocity of planet about sun 3 Angular momentum of planet about sun All of these

A particle of mass m is executing a uniform motion along a circular path of radius r If the magnitude of its linear momentum is p the radial force acting on the particle will be 1 pmr 2 rm p 3 mp r 4 p mr

A car of mass 1000 kg moves on a circular track of radius 40 m If the coefficient of friction is 1 28 the maximum velocity with which the car can be moved is 1 22 4 m s 2 112 m s 3 0 64x40 TO00X100 4 1000 m s m s

Two satellites are orbiting Earth The path of one satellite has the equation x2 y2 56 250 000 The orbit of the other satellite is 200 km farther from the centre of Earth In one orbit how much farther does the second satellite travel than the first satellite

The path of projectile is represented by y Px Qx Column II P P Q Q P R P 140 Column 1 A Range B Maximum height C Time of flight D Tangent of angle of the projection is S 2 Vog

3 A particle of mass m is moving in a vertical circle of radius r If the velocity of the particle at the uppermost point is 2gr then its velocity at the lowermost point 1 7 gr 2 6gr V 3 5gr 4 2 gr 4 24 T

A hemispherical bowl is placed in inverted position on a frictionless horizontal floor and a small disk is placed on the top of the bowl as shown in the figure The disk and the bowl are of equal mass and there is no friction between them The disk is slightly pushed horizontally so that it starts sliding on the bowl with negligible speed Find the angle with the vertical axis of bowl at which disk leaves the bowl

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 u 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 u 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 22 7

If a particle is moving along a curved path Then component of acceleration along velocity is known as tangential acceleration and perpendicular to velocity is known as normal acceleration Now consider a particle with velocity 4 3 and acceleration 103 Then 9 Tangential acceleration vector is A 4 31 10 B 4 3 Magnitude of normal acceleration is B 6 A 10 C 8 8 D 41 3 D 5 2 CLOSE

75 min 25 secs 50 A solid disc of radius 5 cm rolls without slipping on a horizontal floor as shown with an angular velocity of 3 rad s and angular acceleration of 2 rad The magnitude of acceleration of point P on the disc at the given instant is in cm s Type your answer here

A bug crawls at a constant rate vo along the spoke of a bicycle wheel of radius R the bicycle is moving with a speed u Find the magnitude of component of acceleration along the spoke in the form of r the distance from centre of wheel A ru R Correct answer

Use your brain power As a civil engineer you are given contract to construct a curved road in a ghat In order to obtain the banking angle you need to decide the speed limit How will you decide the values of speed v and radius r

If a 8 0 08 and b 6 0 06 Let x a b y a b z axb The correct order of error in x y and z 1 3 Correct Answer 3 x y z x y z x z y x z y F 4020 67

Consider a thin stick of length L standing on one of its ends on a frictionless surface It is slightly pushed at the other end of the rod Then path of centre of mass of the rod is A x 0 C y 0 B x y x 2 X D 2 L 4 L 4 2 y 1 L

4 A circular disc of radius R is rotating about its axis O with a uniform angular velocity o rad s as shown in the figure The magnitude of the relative velocity of point A relative to point B on the disc is a zero c 2R00 sin G ope 30 A 0 d 3 Roo sin b Roosin

3 580 K 4 145 K 5 A particle revolves with constant angular acceleration trad s If the particle starts from rest how many revolution will it make in the first 10 4 25 seconds 1 16 2 10 3 20 16 3 580 K 4 145 K ford s 10 1 16 3 20 2 10 4 25

A uniform disc of mass m and radius R is kept on frictionless horizontal surface The Figure shows top view of the smooth surface Two particles each of mass m are connected to the disc by two identical light inextensible strings as shown in the figure The particles are given velocity Vo perpendicular to the length of strings Select the correct the alternatives for the moment just after the projection A Acceleration of the particle will be SPE C Tension in the strings is 2R mV2 V 2R Vo Vo 2R B Angular acceleration of disc will be D Tension in the strings is mv 2V2 0 5R

30 A particle of mass m is moving with a uniform speed v on a circular path of radius R The magnitude of change in acceleration of the particle in going from P to P is 1 3 Zero 2v R P 2 2 4 v P 2R 2 v R D

A wheel is subjected to uniform angular acceleration about its axis Initially its angular velocity is zero In the first two seconds it rotates through an angle 0 In the next two seconds it rotates through an additional angle 02 What is the ratio of 0 0 is O O 1 2

A fixed ring of mass m has two beads A B of mass m each both being able to slide on the ring without friction Initially the ring lies on a frictionless horizontal table and the beads are given velocities vo relative to the ring in the same direction The initial relative acceleration of the beads w r t each other where R is the radius of the ring

An object starts moving from rest on a circle of radius 2m with constant tangential acceleration 2m s The time after which acceleration of object makes angle 45 from tangent is 0 1 sec O 2 sec O 2 sec 15 12 01 sec

A particle of charge q and mass m at t 0 enters in a uniform magnetic field B Bk while moving with velocity v v i k then mv 1 it moves along a circular path of radius qB 2xm 2 it moves along a helical path of pitch qB 3 it moves along a helical path of pitch 2 2mm qB 4 it moves along straight line path along z axis

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length The other end is fixed The system is given an angular speed es about the fixed end of the spring such that it rotates in a circle in gravity free space Then the stretch in the spring is 1 3 m co k moo m o om 2 mfer k me m k moo

A particle of mass m is moving in horizontal circle of radius r with uniform speed v When it moves from one point to a diametrically opposite point its A KE changes by mv B KE changes by mv 1 4 C momentum does not change momontumchangos by 2mi

An ideal string is wound around a cylinder the other end of the string is fixed on a wall The cylinder lies on a rough horizontal surface The surface is moved with constant velocity v as shown in figure There is no slipping between string and cylinder The cylinder rolls without slipping on the surface Choose the correct option S O The velocity of the axis of the cylinder at the instant the string makes on angle 8 with the vertical is V 1 sin 0 V The velocity of the axis of the cylinder at the instant the string makes an angle 8 with the vertical is 2 sin 0 The acceleration of centre of cylinder is non zero V The angular velocity of cylinder is where R is radius of cylinder

Question 5 20 pts In Fig 3 a solid sphere of radius R 5 cm and mass M 2 kg rolls from rest a D 50 cm distance down a 0 30 incline Assume that the incline and the horizontal surface have the same fictional coefficient a Compute the angular velocity at the bottom of the incline b Determine the angular acceleration of the sphere on the incline c If the sphere and a marble of radius r 5 mm release together from rest at the initial location is the sphere s time to the bottom more than less than or the same as the marble s why 0 Fig 3

9 A car is moving on a circular level road with radius of curvature 300m If the coefficient of friction is 0 3 and acceleration due to gravity is 10m s2 the maximum speed of car can be 1 90 km h 2 81 km h 3 108 km h 4 162 km h

2 Three metallic rods of identical lengths and cross section area are welded together to form the letter Y of English alphabet If their conductivities are in the ratio k 2k 3k and their peripheral temperatures are 60 C 51 C and 20 C respectively as shown then the junction temperature will be 60 C 1 35 Junction k 3k 51 C 2k 20 C 2 37 C Aal Medical Divis

A person moves towards north with uniformi speed of 17 m s and cover 16 m After this hel moves towards east and covers 8 m and finally covers 10 m distance with same speed in south Find out 1 Distance travelled by person ii Displacement of person iii Average velocity of person

Two rings A B are of radius R each Ring A is at rest while ring B rotates about point O which is one of the intersectio points of the two rings with constant angular velocity w The speed of the other intersection point O has a maximum value 2w R has a constant value wR has a minimum value w R has a constant value 2wR A D B

A driver applies the brakes on seeing the red traffic signal 400 m ahead At the time of applying the brakes the vehicle was moving with 15 m s and at retarding 0 3 m s The distance covered by the vehicle from the traffic light 1 min after application of brakes is O O 25 m 375 m 360 m 10 m

A very long straight current carrying wire is along z axis passing through origin as shown It applies a magnetic force of interaction on a 1 with a b in the first quadran quarter elliptical segment given by of xy plane carrying a current i a b 0 b a 0 Of magnitude Holi In Of magnitude of in Holi In 4 a b In the direction of I b In the direction of k