Circular Motion Questions and Answers

The pressure on a circular plate is measured by measuring the force on the plate and the radius of the plate If the errors in measurement of the force and the radius are 5 and 3 respectively the percentage of error in the measurement of pressure is O O 8 14 11

Four wheeler is moving with a uniform speed on a level road There is a balloon filled with helium and attached to a piece of string tied to the floor inside the four wheeler The string is observed to be vertical While maintaining the speed on the level road the four wheeler takes a left turn then determine the position of the balloon It burst while taking the curve It continue to remain vertical It is thrown to the left side It is thrown to the right side

A ball is projected from point A with a velocity 10 m s perpendicular to the inclined plane as shown in the figure Range of the ball on the inclined plane is A B C D co 15 40 20 13 13 20 13 40 m m m m 30

Question No 23 A particle covers equal distance around a circular path in equal intervals of time particle remains constant with time O Acceleration O Velocity O Speed O Displacement quantity connected with the motion of

1500 kg car drives around a flat 220 m iameter circular track at 22 m s Part A What is the magnitude of the net force on the car Express your answer using two significant figure

A uniform rigid rod of mass m and length is gently held on a smooth fixed inclined plane of angle of inclination 0 with its length perpendicular to inclined plane by an external agency as shown in figure external agency is not shown in the figure The angular acceleration of rod just after the external agency is removed is A 3g sin 0 21 B 6g sin 0 2g sin 0 D zero

A stationary horizontal uniform circular disc of mass m and radius R can freely rotate about its axis Now it starts experiencing a torque T a b where is the angular displacement of disc and a and b are positive constants Find the angular velocity of the disc as a function of 0

A particle starts from rest at O and moves along a horizontal semi circular track OAB of radius R Im as shown in the figure The rate of change of speed of the particle is constant and equals to 2m s A is a point lying exactly on the middle of semicircular track as shown in figure When the particle reaches A Find a The magnitude of velocity vector of the particle at the instant b Magnitude of acceleration vector of the particle at the instant c The cosine of angle between acceleration and velocity vector of the particle at that instant ke A X

A particle of mass m revolves in a circle of radius R with a uniform angular speed w Apart from ground frame it is also observed from a frame rotating about the same axis with a uniform angular speed wo in same sense The acceleration of particle as observed in the rotating frame is w R R The acceleration of particle as observed in the rotating frame is w wo R O The acceleration of particle as observed in the ground frame is w R The acceleration of particle as observed in the ground frame is w R

A mass is attached to one end of a massless string the other end of which is attached to a fixed support The mass swings around in a vertical circle as shown in figure Assuming that the mass has the minimum speed necessary at the top of the circle to keep the string from going slack at what location 8 in degree should you cut the string so that the resulting projectile motion of the mass has its maximum height located directly above the center of the circle Fill 0 in OMR sheet 15 cut 0

R 2 The solid part has a uniform charge density p and cavity has no charge If the electric potential at A and magnitude of 5pR PR electric field at point C are and XEO YEO then value of is X A R R 2 B

Q22 A balloon is ascending vertically with an acceleration of 0 2 m s 2 Two stones are dropped from it at an interval of 2 sec Find the distance between them 1 5 sec after the second stone is released use g 9 8 m s

A thin uniform ring of mass m and radius R lies on a smooth horizontal x y plane at rest A particle of equal mass m moving along positive x direction strikes the ring tangentially and sticks to it If velocity of the particle just after the collision is Kvo then find k 3 m Ring m X

cle is moving in a circle of radius R 3 m with an angular speed 2 radian per second in clockwise direction as given in the diagram The acceleration in m s of particle at point P is 1 61 6 3j 3 61 6 3 P 60 X 2 6 31 61 4 61 6 3j

A particle of mass 2 kg is moving in a circular path of radius 1 m with speed v 2t where u is in ms and t is in s Magnitude of tangential force acting on the particle is 1 2 N 3 8 N 2 1 N 4 4 N

In a system a particle A of mass m and charge 2q is moving in the nearest orbit around a very heavy particle B having charge q Assuming Bohr s model of the atom to be applicable to this system the orbital angular velocity of the particle A is AP EAMCET 2019 1 22 2 m q E h4 2 32 3 m q 3 h

A rigid horizontal smooth rod AB of mass 0 75 kg and length 40 cm can rotate freely fixed vertical axis through its mid point O Two rings each of mass 1 kg are initially at rest at a distance of 10 cm from O on either side of the rod The rod is set in rotation with an angular velocity of 30 radians per second Find the velocity of each ring along the length of the rod in m s when they reach the ends of the rod

10 A block of mass m slides down on inclined wedge of same mass m as shown in figure Friction is absent everywhere Acceleration of centre of mass of the block and wedge is a zero c g cos 0 1 sin 0 d 77 m g sin e 1 sin 0 g sine 1 cos 0 0

In a water park there is a circular river in which the flow is at a speed u along a circular path A small toy boat is steered radially with speed v relative to water If reaches a diametrically opposite point B on the other bank in half round 180 The time to cross the river and reach B is r is radius of central circle 0 VI A e 1 V VIL C e eu B V D None of these 0r B

Kepler s third law states that square of period of revolution 7 of a planet around the sun is proportional to third power of average distance r between sun and planet i e T K here Kis constant If the masses of sun and planet are M and m respectively then as per Newton s law of gravitation force of attraction between them is here G is gravitational constant F GMM

A uniform wire is bent in the form of a circle of radius r 0 4m It is initially at rest and its diameter OA is horizontal It is then released and allowed to swing about point O in the vertical plane During its motion when the diameter occupies the position OB then its angular speed is rad sec

In a double star system two stars of masses m and m separated by a distance d rotate about their center of mass Then their common angular velocity would be A B Gmi d Gm d

2 A particle of mass m is moving in a circular path of fixed radius r such that its centripetal acceleration a is varying with time as a k rt2 where k is constant The power delivered to the particle by the forces acting on it as a function of time t is 1 2 mk r t 2 mk r t 3 1 mk4r2 5 4 O

In a binary system of two particles of unequal masses which of the following quantity is constant for both Angular 1 Linear velocity Angular velocity C

4 A stone of mass 1 kg is tied with a string and i is whirled in a vertical circle of radius 1 m If tension at the highest point is 14 N then velocity at lowest point will be 1 3 m s 2 4 m s 3 6 m s 4 8 m s

Physics Numerical A small sphere B of mass m 1 kg is released from rest in the position show and swings freely in a vertical plane first about O and then about the peg A after the cord comes in contact with the peg The ratio of tension in the cord just before and just after the cord comes in contact with the peg is 9 N where N is 0 8 m 30 0 4m 3 00 B 0 00

MATCHING TYPE WITH 3 COLU was FOUR options A B C and D ONLY ONE of these four options is correct y table has 3 columns and 4 rows Based on table there are THREE questions Each Column I shows four situations with a small ball of mass m connected to an ideal string of length the minimum value of speed u when the string is vertical in order for the mass to complete the and fastened to a point O whose acceleration if any is shown in the diagram Column Il lists circular motion in vertical plane Column III lists the maximum tension throughout the circular motion corresponding to minimum speed Column 0 3 E MEGACOS III IV 0 19 3 O l O 45 3 A 1 iii P C II i R u U 1 A III ii P C IV iv R 2g U 1 iii Column 2 1 29 3 1 iv 3g 5ge Pick the correct combination from given options A 1 ii P C III ii Q 20gf 3 P 6 mg Column 3 Q 4 3 mg B II iv R D IV ii P Pick the option for combination where maximum tension occurs at 0 0 with vertical B II ii Q D 1 iv S R 7 mg B II ii R D IV i P S 8 mg Pick the correct combination where maximum tension position occurs at greatest possible angle from vertical POWE

A 10 kg ball attached to the end of a rigid massless rod of length 1 m rotates at constant speed in a horizontal circle of radius 0 5 m and period n 2 sec as in fig The horizontal force exerted by rod in N on the ball is F Fill F 16 in OMR sheet 2 L 10kg

A point mass mis fixed rigidly to the rim of a thin circular disc of radius R The disc is pivoted at its centre so that it can rotate in the vertical plane Using a motor the disc in the clockwise direction Let the instantaneous angular position of the point mass bea with its bottom most position is rotated with a constant angular velocity shown in the figure on the right beinge 0 Let the force exerted by the disc on the point mass be denoted by F 8 and let the instantaneous power being delivered by the disc to the point mass be denoted by P e Which of these options is are correct 0 F x O P 3n mg Ro 2 mgRoo

11 A particle starts moving on a circular path from the rest such that its tangential acceleration varies with time as a kt Distance travelled by particle on the circular path in time t is A B C kt 3 kt3 6 D kt 6 kt

34 A small source of sound moves on a circle as shown in the be the frequencies heard when the source is at A B and C respectively Then 1 2 a n n nz c n n n3 B ACI V b n nz n d n n 13

A train 1 moves from rest east to west and another train 2 moves from west to east on the equator with a a2 equal speeds relative to ground The ratio of their centripetal accelerations is A 1 B 1 C 1 relative to centre of earth D 1

21 Consider the L shaped bar shown in figure At the instant shown the bar is rotating at 4 rad s and is slowing down at the rate of 2 rad s Aff Motor y axis 2 m B 2m n T A x axis a Find the acceleration of point A b Find the relativo acceleration a of point B with respect to point A at ca I 1 28 2 4 a w y 1 x 2 3 it Da

A body of mass 100 grams is tied to one end of a string and revolved along a circular path in the horizontal plane The radius of the circle is 50 cm If the body revolves with a constant angular speed of 20 rad s find the i period of revolution ii linear speed iii centripetal acceleration of the body 3 marks

A pendulum bob of mass m connected with a string of length lies in vertical plane It is given just sufficient velocity so as to complete vertical circle Mark the CORRECT statements C Net impulse as bob moves from A to B has magnitude m 8mgl Net workdone by all the forces as bob moves from A to B is mgl Net acceleration at B has magnitude 10g Taking top most point as reference total mechanical energy is mge 2 D A B

A car is travelling with a speed of 90 m s due east An observer is present at 5 m south of the line of motion Find the angular velocity in rad sec of car relative to t observer when car is located northeast of him

Wind is blowing with velocity V towards north east A man starts running towards north with acceleration a The time after which man will feel the wind blowing towards east is O O V za VIA O Zv

Q 2 A ceiling fan is spinnning at 416 rpm just before you turn it off It comes to rest smoothly over 17 3 s How many revolutions does it make as it stops 60 0 revolutions 9 55 revolutions 377 revolutions 754 revolutions

A ball is moving in a circle at fixed speed which statement is true no acceleration present only force act acceleration present but constant magnitude acceleration present and act like tangent to circle

Q 3 The loop the loop section of a particular roller coaster has a radius of 19 5 m Riders while going around this circular part of the track experience an acceleration of 3g where g is the free fall acceleration How fast does the cart travel around the track Assume it travels at constant speed 1 51 m s 13 8 m s 84 9 m s 0 m s

A particle is moving on a circular path with constant speed v It moves between two points A and B which subtends an angle 60 at the centre of circle The magnitude of change in its velocity and change in magnitude of its velocity during motion from A to 3 are respectively 1 Zero Zero 3 O 2 V 0 4 2v v

10 An alpha particle is moving perpendicular to the uniform magnetic field of 0 5 T with the velocity 3x 10 ms What is the work done by the particle a 15x10 J c3J d Zern b Infinity d Zero

7 a On a curvy road a motorist applies breaks and the speed of the vehicle reduced uniformly from 60 km h at point A to 40 km h at point B the points A and B are 120 m apart If the vehicle has a resultant acceleration of 2 5 m s at point A calculate the radius of the curvature of the road at this point Calculate also the acceleration of the vehicle at point B where the road has a radius of curvature equal to 90 m

A small particle of mass M is released from rest from point A inside a frictionless fixed hemispherical bowl as shown The graph between t ratio r of magnitude of centripetal force and normal reaction on the particle at any point on the bowl as a function of cos is A DA B R N 1 C cose 1 cose H

A mass m is attached to a thin wire and whirled in a vertical circle The wire is most likely to break when NEET 2019 1 The mass is at the highest point 2 The wire is horizontal 3 The mass is at the lowest point TE 4 Inclined at an angle of 60 from vertical

A uniform ring of radius 1m is performing rolling motion on the horizontal surface as shown in the figure Att 0 acceleration of COM of ring is 31 m s while angular acceleration angular velocity are 3 k radis and 2 k rad s where x z plane is horizontal and y is vertical axis A is in contact with surface and C is at 2m above the surface B and D are 1m above the surface J B 0 A D

pulleys A and B as shown in the figure The pulleys are mounted on two fixed horizontal axles Radii of the pulleys A and B are 50 cm and 80 cm respectively Pulley A is driven at constant angular acceleration of 0 8 rad s until pulley B acquires an angular velocity of 10 rad s The belt does not slide on either of the pulleys Sliding alesent ja same a Find the acceleration of a point C on the belt and angular acceleration of the pulley B b How long does it take for the pulley B to acquire an angular velocity of 10 rad s Solution ac Since the belt does not slide on the pulleys magnitudes of velocity and acceleration of any point on the belt are same as that of any point on the periphery of either of the two pulleys a ax ac ATA BB Substituting A we have 0 5 m r 0 8m and 0 8 rad s CATA 0 5 rad s 0 4 m s and ag TB B at t 0B 0Bo OB ac TB On 1 20

A disc of mass m is rotating in horizontal plane about a vertical axis passing through its centre with angular velocity wo A small block of mass m stick to the circumference of disc then new angular velocity of disc will be O wo 2 O 2wo 3

In the figure the block on the smooth table is set into motion in a circular orbit of radius r around the centre hole The hanging mass identical to the mass on the table and remains in equilibrium Neglect friction The string connecting the two blocks is massless and inextensible Select the correct answer s P The angular speed w of the block in its circular motion is Kinetic energy as function of r is given by mgr 2 O Angular momentum about the hole is conserved even if hanging block is pulled down The block on table is in equilibrium

A small ball attached with light string is given 7 a velocity gl at the lowest point of verticle circle Find the maximum height reached by the ball 40 B 50 7 gl U 2 30 D 270