Circular Motion Questions and Answers

Two cylinder A and B having piston connected by massless rod as shown in fig The cross section are of two cylinder are same and equal to s The cylinder A contains m gm of an ideal gas at pressure Po and Temperature To the cylinder B contain identical gas at same temperature To but has different mass The piston is held at the stare in the position so that volume of gas in cylinder A and cylinder B are same and is equal to Vo The walls and piston of cylinder A are thermally insulated whereas cylinder B is maintained at temperature To reservoir The whole system is vacume Now the piston is slowly released and it moves towards left and mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes then here y for the gas 1 5 The mass of gas in cylinder B ZZZZZZ

3 r A cyclist taking turn bends inwards while a car passenger taking same turn is thrown outwards The reason is 1 Car is heavier than cycle 2 Car has four wheels while cycle has only two 3 Difference in the speed of the two 4 Cyclist has to counteract the centrifugal force while in the case of car only the passenger is thrown by this force

A disc of radius R rolls on a horizontal surface with linear velocity V and angular velocity S There is a point P on circumference of disc at angle with upward vertical diameter measured in anticlockwise sense as shown in the figure which has only vertical component of velocity Here is equal to A si sin 1 RS f B sir P R 0 fov 1 C f cos V R 1 D f cos V RS

5 The radius of circle the period of position and sense of revolution are indicated in the figure y 2 y t 4 sin 3 y t 3 cos Flo 4 y t 3 cos y projection of the radius vector of rotating particle Pis NEET 2019 1 y t 3 cos2nt where y in m t 2 P t 0 3 t 2 3 m 7 2 T 4 s where y in m where y in m where y in m

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac varies with time t as ac k rt where k is a constant The power delivered to the particles by the force acting on it is A 2 mk r t B mk r t C mk r 45 3

A cylinder rolling with an attached Mass A small mass m is attached to a ring of same mass and radius R The ring rolls without sliding over a horizontal plane When the attached mass is at lowest position ring centre is moving at speed v At what maximum value of v the ring moves without bouncing R

Consider a particle undergoing a uniform circular motion along a circle of radiusm with a speed of 5 m s The magnitude of change in velocity in a time duration of 4 s will be 6 m s O 5 2m s 10 m s Zero

A 0 5 kg ball attached to a 2 1 m long string is swung in a vertical circle If at the bottom the ball possesses three times the speed it has at the top of the circle and takes 0 7 s to move from the top to the bottom of the circle in a clockwise direction determine the following The minimum speed at the top required to keep the ball in a circular motion Select one 4 5 m s 20 6 m s 0 m s 9 8 m s O O O O

One end of a stick with mass m and length is pivoted on a wall and the other end rests on a frictionless floor as shown in figure Let F and FR be the vertical forces on the left and right ends of the stick respectively Then Pivot FL A FL mg 2 C FL FR FRE B FL FR D FL FR mg cos 0

2 Chhota Bhim can swim with a speed of 10 m s w r t river which is flowing at a speed of 5 m s The time taken by Chhota Bhim in crossing the river in minimum time will be width of river 200 m 1 20 s X 40 3 S 20 2 S 3 4 40 s

The track in the vertical plane consists of three segments 1 AB inclined at 0 tan 1 and coefficient of 2 1 friction merges smoothly into a u 4 9 smooth parabolic track BO given by equation x 4y O is the origin OC smooth semicircular track of radius R 0 5m The minimum height h in m at which a particle is to be released from rest so that it successfully completes the semicircular travel is Use g 10 ms 2

seconds is el Question Type Single Correct Type 16 28 3 10 4 12

A stone tied to the end of a 80 cm long string is whirled in a horizontal circle with a constant speed If the stone makes 14 revolutions in 25 s the magnitude of its acceleration is Question Type Single Correct Type 120 m s 2 12 m s 3 9 9 m s 48 m s

1 81 C 2 900 C 3 627 C 4 450 C When a copper ball is heated the largest percentage increase will occur in its 1 diameter 2 area 3 volume 4 density For a particle of a purely rotating body v roo so correct relation will be 1 a x 2 C B 3 vx 4 is independent of r Two rings of same radius r and mass m are placed such that their centres are at a common

A particle of mass m is fixed at the lower end of a massless rod The rod is given a velocity 4gl at the lower most position Calculate the compression in the rod at the topmost position 0 2 2mg 3 4mg 4 mg b hill

4 The angular displacement of a rotating wheel 3 is described by the equation 0 0 at bt where it is time and o a and b are positive constants The angular acceleration of the wheel as a function of time t is A equal to a positive constant B zero C 2a 6bt D 2at 3b1 E 01 1 3 ap bi

A rod of length is travelling with velocity UCM and rotating with angular A we velocity such that UCM The distance covered by the point B when the 2 rod completes one full rotation is ne find the value of n K 1

A small sphere undergoes vertical inside a smooth vertical tube where sphere just fits inside the tube as shown in the diagram Calculate minimum speed required at the bottom most so that it could go in the complete loop J 5gR 3 3gR R v 2 4gR 4 6qR

A stone of mass m is tied to a string and is moved in a vertical circle of radius r and has angular velocity n rev min at bottom most point The tension in the string when the stone is at the lowest point is 1 mg 3 m g nr 2 m g nr Las m g 7 n r 900

26 A parallel plate capacitor completely filled with a dielectric sheet of thickness d and relative permittivity is placed on a horizontal tabletop The lower plate is glued with the tabletop and the dielectric slab is glued with the lower plate The plates are square of edge length I and mass of the upper plate is m The plates are given charges q and q then the upper plate is shifted horizontally by a small distance x along one of its edges and set free Find period of oscillation of this plate Thickness d of the dielectric is much smaller than the edge length 1 Ane 88 Erfomek

Two beams of red and violet colours are made to pass separately through a prism angle of the prism is 60 In the position of minimum deviation the angle of refraction will be a 30 for both the colours 2008 3M b greater for the violet colour c greater for the red colour d equal but not 30 for both the colours

62 25 cm and 32 25 cm 10 The expansion of an ideal gas of mass m at a constant pressure p is given by the straight line B Then the expansion of the same ideal gas of mass 2m at a pressure 2p is given by the straight line a C c B Volume K W B C Temperature b A d data insufficient 974 eeloitte wol al Calw n

2 A small sphere hangs from a string attached to the ceiling of a uniformly accelerating train car It is observed that the string makes an angle of 37 with respect to the vertical The magnitude of the acceleration a of the train car is most nearly m r 10 HR A B 2 6 0 m s 7 5 m s 8 0 m s D 10 m s P Ber Tops on ves com

130 mm H 250 mm Z lc 250 mm B 05 E D 130 mm X Two disks each of 130 mm radius are welded to the 500 mm rod CD The rod and disks unit rotates at the constant rate w2 29 rad s with respect to arm AB Knowing that at the instant shown w 9 rad s determine the magnitude of the velocity of Point E in m s to two decimal places N

A conducting rod of length 2l is rotating with constant angular speed W about its perpendicular bisector A uniform magnetic field B exists parallel to the axis of rotation The emf induced between two ends of the rod is Question Type Single Correct Type 1 Bwl2 1 2 2 Bwl B 1 3 Bwl 8

Crank OA rotating around point O leads to movement of wheel 1 of radius R 20 cm rolling inside circle surface 2 Wheel 1 in contact with wheel 3 makes it spin around points O Fig Find the ratio r 10 cm A 1 of angular speed of wheel 3 and that of crank OA if the radius of wheel 3 is 1 B 2 C 3 Space for Rough Work D 6

The strings AB and AC each of length 60 cm connect a ball of mass 400 g to a vertical shaf as shown When the shaft rotates at a constant angular speed w the ball travels in a horizontal circle with the strings inclined at y 30 to the shaft If the tension in the string AC is 6 N that in the string AB and the angular speed w respectively are B I C A 10 62 N and 8 32 rad s 9 92 N and 5 32 rad s 6 92 N and 9 32 rad s

A small body of mass m is at rest inside a thin narrow tyre of mass m and radius r which is lying on a horizontal table with its plane horizontal How does the centre of mass of the system move if the smal body is given a tangential initial velocity v at t 0 as shown in figure If after time T the velocity of tyre becomes zero then find T Find magnitude of velocity of ball at t T 6 Neglect friction everywhere E r Vo

Question 3 The weight of substance deposited is 1 34 g calculate current in amperes when the process of electrolysis is carried for 10 minutes Given ECE 0 001118 4 Ampere 2 Ampere 1 Ampere

A uniform disc of mass m and radius R is free to rotate about its fixed horizontal axis without friction There is sufficient friction between the inextensible light string and disc to prevent slipping of string over 3mg disc At the shown instant extension in light spring is where m is mass of block g is acceleration K due to gravity and K is spring constant Then select the correct alternative s www 000000 m R m A Acceleration of block just after it is released is 4g 3 B Tension in the string continuously increases till extension in the spring reaches maximum value 3 C Acceleration of the block just after release g 4g D Angular acceleration of disc just after release is 3R

A stone is dropped from a certain height After falling for 5 s the stone breaks through a pane of glass and instantaneously loses half of its velocity If the stone then takes one more second to reach the ground determine the height in metre of glass above the ground g 10 m s

A particle moves along an arc of a circle of radius R Its velocity depends on the distance covered as v a s where a is a constant then the angle a between the vector of the total acceleration and the vector of velocity as a function of s will be 1 tana 2 tana 3 tana 4 tana R 2s 2s R 2R S S

A body of mass m is moving in a circle of radius r with a constant speed v The force on the body mv and is directed towards the centre What r is the work done by this force in moving the body over half the circumference of the circle is 1 3 mv r my X r 2 Zero 2 r 4

One end of string of length is connected to a particle of mass m and the other end is connected to a small peg on a smooth horizontal table If the particle moves in circle with speed v the net force on the particle directed towards centre will be T represents the tension in the string Question Type Single Correct Type 1 2 T T mv e mv e

A uniform circular disc of mass 2m and radius R placed freely on a horizontal smooth surface as shown in the figure A particle of mass m is connected to the circumference of the disc with a massless string Now an impulse J is applied on the particle in the directions shown by dotted line The acceleration of centre of mass of the disc just after application of impulse is If J 10 N sec m 10 kg and R 25 cm A 1 m s C 3 m s B 2 m s D 4 m s 2R R m 2m

A racing car is traveling along a straight track at a constant velocity of 40 m s A fixed TV camera is recording the event as shown in figure In order to keep the car in view in the position shown the angular speed with which the camera should be rotated is A 4 3 rad s C 8 3 3 rad s B 3 4 rad s D 1 rad s 30m 30 40m s

1 Car A can travel around a curved section of road without skidding at a maximum constant speed of 10 m s When car B travels around the same curve without skidding at its maximum speed it has twice the centripetal acceleration as car A The maximum speed at which car B can safely travel around the curve is most nearly A 5 0 m s B 10 m s C 14 m s D 20 m s E 28 m s or 10 HP PO

A park has a radius of 10 m If a vehicle goes round it at an average speed of 18 km hr what should be the proper angle of banking If the road of the previous problem is horizontal no banking what should be the minimum friction coefficient so that a scooter going at 18 km hr does not skid

Find the acceleration of a particle placed on the surface of the earth at the equator due to earth s rotation The diameter of earth 12800 km and it takes 24 hours for the earth to complete one revolution about its axis

Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 km s a The average velocity of the earth from 1st Jan 90 to 30th June 90 is zero b The average acceleration during the above period is 60 km s 2 c The average speed from 1st Jan 90 to 31st Dec 90 is zero d The instantaneous acceleration of the earth points towards the sun

A car of mass M is moving on a horizontal circular path of radius r At an instant its speed is u and is increasing at a rate a a The acceleration of the car is towards the centre of the path b The magnitude of the frictional force on the car is mu greater than c The friction coefficient between the ground and the car is not less than a g d The friction coefficient between the ground and the car is tan r 2 1 V 2 rg

A stone of mass m tied to a string of length is rotated in a circle with the other end of the string as the centre The speed of the stone is v If the string breaks the stone will move a towards the centre c along a tangent b away from the centre d will stop

5 A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting The car moves up along an inclined cliff at a speed u and makes a jump to leave the cliff and lands at some distance Let R be the maximum height of the car from the top of the cliff The tension in the string when the car is in air is a mg b mg mv R 2 c mg mu R 2 d zero

5 A particle of mass m rotates with a uniform angular speed o It is viewed from a frame rotating about the Z axis with a uniform angular speed wo The centrifugal force on the particle is 2 2 a mw a b mwa c m o 2 2 a d mw w a

3 A car leaves a stop sign and exhibits a constant acceleration of 0 250 m s parallel to the roadway The car passes over a rise in the roadway such that the top of the rise is shaped like an arc of a circle of radius 450 m At the moment the car is at the top of the rise its velocity vector is horizontal and has a magnitude of 6 50 m s What are the magnitude and direction of the total acceleration vector for the car at this instant 10 points a 0 250 m s 7 6 50 m s

A particle of mass m is placed at a distance of 4R from the centre of a huge uniform sphere of mass M and radius R A sp rical cavity of diameter Ris made in the sphere as shown in the figure If th gravitational interaction potential energy of the system of mass manche remaining sphere after making XGMm 28R the cavity is Find the value of A Type your answer here R 4R 7

An object moves uniformly around a circular path of radius 18 0 cm making one complete revolution every 2 15 a What is the translational speed of the object m s b What is the frequency of motion in hertz Hz c What is the angular speed of the object rad s

ALLEN For a body in a circular motion with a constant angular velocity the magnitude of the average accel over a period of half a revolution is times the magnitude of its instantaneous acceleration 2 B 7 2 A T C T D 2 The plane of rotation is xy At a certain instant the acceleration

9 A small heavy block is attached to the lower end of a light rod of length which can be rotated about its clamped upper end What minimum horizontal velocity should the block be given so that it moves in a complete vertical circle oooooo A m 40 m 48 00 B

e notaz 10 Note Figure not drawn to scale A car is traveling clockwise around a circular racetrack of radius 1440 m When the car is at the northernmost point on the circle as shown above it has a speed of 36 0 m s and is slowing down at a rate of 1 20 m s 4 The direction of the velocity of the car A due east B south of east C due south D south of west E due west Single son Usage MY 5 The direction of the acceleration of the car is A due east B south of east C due south