Circular Motion Questions and Answers

is rotating about a vertical axis in the plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad s Distance of the S A particle horizontal particle from axis is given by R R t where t stands for time The speed of the particle as a function of time is a B 1 c B B B 2 b R Bt d B R Ro

The electric field at the origin is along the positive x axis A small circle is drawn with the centre at the origin cutting the axes at points A B C and D having coordinates a 0 0 a a 0 0 a respectively Out of the points on the periphery of the circle the potential is minimum at a A b B c C d D

A particle of mass m describes a circle of radius r The centripetal acceleration of the particle is 4 r2 The momentum of the particle is O 4m O2m EN O 4m O2m

Negative Marks Two moving particles P and Q are 10m apart at a certain instant The velocity of P is 8 m s making 30 with the line joining P and Q and that of Q is 6 m s making 30 with PQ in the figure Then the angular velocity o respect to P in rad s at that instant is O 0 O 0 1 1 In all other cases O 0 4 P 30 10m 8m s Q 6m s 30 Sav

Some cases regarding vertical circular motion each circular path is having radius R are shown in Column 1 Column 2 shows tension normal at point B While column 3 indicates Information regarding path and motion Column 1 11 III String 60 B u 2gR String String B 3gR Fixed i ii iii Column II Tension Normal at point B is zero Tension Normal at B is 2mg Tension Normal at 3mg point B is 2 P Q R Column Ill Path will be circular Motion will be complete vertical circular motion Motion will be oscillatory Motion will Save Next

rotation 27 An electron with mass m velocity v and charge e describing half a revolution in a circle of radius r in a magnetic field B will experience change in energy equal to 1 1 mv 4 1 2 Brev

Particles P and Q are undergoing uniform h orizontal circular motion along concentric ci rcles of different radii in clockwise sense P completes each round in 2 min while Q doe s it in 5 min time to make one revolution aro und P is

A small block of mass 1 kg is being moved with constant speed of 10 m s on a typical path in a x y vertical plane whose equation is y The coefficient of friction between the block and path is 0 01 Find the magnitude of power dissipated by frictiona force in watt at x 2 m 30 10

A rod of length is pivoted at one of the ends 18 and is made to rotate in a horizontal plane as shown in figure with a constant angular speed A ball of mass m suspended by a string of length from the other end of the rod If the angle made by the string with the vertical is 6 then angular speed of rotation is 1 3 1 sin 0 g tan 0 1 sin 0 2 4 cos 0 m g cot 0 1 cot 0 fa af de 3 qui fait qe e ai t gi n i Herial l m Zour i ra i 1 3 g 1 sin 0 a f t u y c g st un fond oft and g tan 0 1 sin 0 2 4 g cos 0 m g cot 0 VE 1 cot 0 qui

25 180 In circular motion The centripetal acceleration is Due to change in magnitude of velocity only Due to change in direction of velocity only Due to change in both magnitude and direction of velocity Neither due to change in magnitude of velocity nor due to change indirecti

The materials suitable for making electromagnets sho have a high retentivity and high coercivity b low retentivity and low coercivity c high retentivity and low coercivity d low retentivity and high coercivity

Figure shows the initial velocity and acceleration of a body The direction and absolute value of the acceleration remain constant Find the time and radius of curvature when the velocity reaches its minimum value Remin Vo cos a v sin a

A particle starts moving with velocity v 1 m s and acceleration a 1 m s radius of curvature of the particle at t 1 sec A 5 m C 675 m String B 5 5 m none m s2 Find the

Why v2 max is root 2g12 For maximum angular displacement 1 2mv 2 2mgl v root 4gl for maximum angular displacement because with this velocity the bob wil not complete full circle but have maximum angular displacement Aug 16 2021 5 47 04 AM Answered A bob of mass m suspended by a string of length I is given a minimum velocity required to complete a full circle in a vertical plane At the highest point it collides elastically with another bob of mass m suspended by a string of length 2 which was initially at rest Both the string are massless and inextensible If the second bob after collision acquires the minimum speed so that bob starts oscillating with maximum possible angular amplitude during its subsequent motion in vertical plane The ratio is Correct answer 02 00

between their centripetal acceleration is 1 R r 2 r R 3 R 4 A particle covers equal distance around a circular 14 path in equal intervals of time Which of the following quantities connected with the motion of the particle remains constant with time 1 Displacement 2 Velocity 3 Speed 4 Acceleration 4 R Radius of the curved road on national highway in ETIT 1 R T fed ft 1 farsang 2 3 4 FRUT 2 r R 3 R 4 r R er fer

20 A bob of mass m is suspended by a light string of 20 length L It is imparted a horizontal velocity v at the lowest point A such that it completes a semicircular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point C Match the column I with column II Am D Column I A Velocity at point V is B Velocity at point B is C Velocity at point C is Ration of kinitic energy at B and C is 1 A p B q C s D r 2 A q B C p D s 3 A B s C 4 D p 4 A s B p C r D q HB Columa II p 3 9 VBL r 5gr 3gL m HR fani mert a Las V I TOEISHUB Dredd HOT Y TINH Vo na mtu ana u organi rasan arafen if it Bao meet thu fing CT Thal GTHL KHI a fami A V B B finant C Cfn Am NI 48 Bargura 1 A p B C s D r 2 A q B C p D s 3 A B C q D p 4 A s B p C D q FII p 3 9 BL r 5gL s 3gL

BEGINNER S BOX particle moves on a circular path of radius r It completes one revolution in 40 s Calculate distance Jacement in 2 min 20 s from point P on the edge of the ground and r 300

For ground to ground projectile time taken b a particle to go from point O to point C is and during the same motion time taken by t particle to go from A to B is T2 then height is y A h E A 8T gT 2 C T 1 B F h C B g T T 3 D T T

A uniform solid sphere rolls up without slipping the rough fixed inclined plane and then back down Which is the correct graph of acceleration a of centre of mass of solid sphere as function of time t for the duration sphere is on the incline Assume that the sphere rolling up has a positive velocity Question Type Single Correct Type 1 F 2 3 BE

Two identical thin rotating rings move along a smooth horizontal plane towards each other Their velocities v and v are directed along a straight line connecting the centers of the rings Angular velocities of the rings o and o Determine the angular velocity of the rings after th ollision if the slipping relative to each other disappears at the last moment a blow A 30 0 4 B 0 110000 30 01 00 30 0 4 D 302 01

1 A 10 kg block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius 10 m The applied force is of 200 N as shown in figure If the block had started from rest at A the velocity at B would be 1 1 7 m s 3 27 m s A 2 15 7 m s 4 34 m s

A charge particle is projected with velocity v 41 31 m s in a region of space where uniform electric field 3 i 5 5 exist Motion of charge particle will be neglect gravity Circular O Helical O Parabolic V m and magnetic field B 81 61 Straight line

Seven identical circular planar disks each of mass M and radius R are welded symmetrically as shown The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is 181 1 MR 2 3 55 2 MR 19 2 4 721 73 2 2 MR MR 0 2018

2 A particle of mass m is fixed to a string of l The particle is given a horizontal velocity of 5gl at the lowermost position Calculate the net acceleration when the string becomes horizontal 1 10g 3 g 12 2 3g 4 2g

12 2 There are two identical balls of mass m 0 2 kg are suspended on two threads of The threads are made of the same material and in their vertical position the two balls touch each other If the ball hanging on the longer thread is released from an initial angle 60 P with respect to the vertical then the thread breaks just before the collision What is the maximum initial angle from which this ball can be released to that none of the threads break after the totally elastic collision A Cos D None of these lengths 1m and C tan B sin 7

Activity No 4 Speed in angles What you need calculator pen and paper What to do Read each item carefully then answer the questions that follow Show your solutions 1 An object travels a distance of 35 ft in 2 7 seconds as it moves along a circle of radius 2 ft Find its linear and angular speed over that time period 2 An object moves at a constant linear speed of 10 m sec around a circle of radius 4 m How large of a central angle does it sweep out in 3 1 seconds with an outer radius of r1 5 cm 71 5 cm

A simple pendulum has length 2m and a bob of mass 100 gram It is whirled in a horizontal plane If the string breaks under a tension of 10 N the angle made by the string with vertical is g 10m s A B O C D cos 0 4 cos 0 1 cos 0 05 cos 0 2

40 A ring of mass m and radius R is being rotated about its axis with angular velocity if to increases then tension in ring 1 Decreases 2 Increases 3 Remains same 4 Zero

30 Two masses m and m are connected by a light rod of length If rod is rotating about an axis with angular speed o Such that its kinetic energy is minimum then its K E is 1 1 m m 2 mm 2 m m cs p 1 mm 00 3 2 m m 4 m 0 31 A body is rolling down an inclined plane If K E of rotation is 40 of K E of translation then body is 1 Ring 2 Disc 3 Solid sphere 4 Hollow sphere 32 A sphere cannot roll on 1 Rough horizontal surface 2 Smooth inclined plane 3 Smooth horizontal surface 4 All of these 33 A solid sphere has combined linear and rotation motion as shown in figure The velocity of its centre of mass when it starts pure rolling is R radius of 1 2 i 1 3 j K 4 00 34 A vector P is along positive x axis if Q is another vector such that PxQ is zero then Q should be 1 5 297 35 The component of the vector 2 3j along the vector B 1 is 2 3 5 2 4 10 2 36 What is the power of an engine which can lift 600 kg of water per minute from 20 m deep well 1 2 kW 2 3 kW

26 A disc of radius R has a concentric hole of radius R 2 an axis through its centre and perpendicular to its plane is 1 23 MR 1 and its mass is M Its moment of inertia about 2 MR

The radius of circle the period of revolution initial position and sense of revolution are indicated in the figure y projection of the radius vector of rotating particle Pis t a y t 3 cos where y in m 2 b y t 3 cos2 t where y in m P 1 0 3 m T 4s

A body moves in a circular path of the radius R with deceleration so that at any moment of time its tangential and normal acceleration are equal in magnitude At the initial moment t 0 the velocity of the body is vo then the velocity of the body after it has moved S at any time will be A B D 2S V Voe R V Voe V Voe V Voe SR 2SR

Three objects A B and C are kept in a straight line on a frictionless horizontal surface They have masses m 2 m and m respectively The object A moves towards B with a speed 9 m s and makes an elastic collision with it Thereafter B makes pefectly inelastic collision with C All motion occur on same straight line The final speed of the object C is m A 1 3 m s 3 5 m s 2m B m C 2 4 m s 4 1 m s

ries LC An inductor 20 mH a capacitor 100 F and a resistor 50 2 are connected in series across a source of emf V 10 sin314t The power loss in the circuit is 1867 916 KES NEET 2018 1 0 79 W 2 0 43 W 3 1 13 W 4 2 74 W should be

17 The two ends of an inextensible string of length I and mass M are fastened together on a circular loop and set spinning about the centre of the circle with uniform angular velocity o The tension in the string is a Mw 1 b Mw 1 2 c Mw Mw 1 47 d

3 On a fixed smooth semicircular ring of radius R one end of a spring of spring constant k and natural length R 3 is attached at end A as shown in the figure The another end of the spring is fixed to a massless bead which can slide without friction on the ring The bead is placed in such a position that the spring makes angle 30 with diameter of AB If the bead is released then the initial acceleration of the bead is The system lies on a horizontal plane KR A B A C 180 J C 2m S 3 1 KR m D kR 3 1 m KR 3m la block F N A

A rear wheel drive car moves with a constant speed v 20 m s on a circular path of radius r 200 m on a horizontal ground Centre of gravity of the car is close to the ground and equidistant from all the four wheels that have negligible mass as compared to rest of the car a What should the minimum coefficient of friction between the tyres and the ground be to make this movement of the car possible

2 3 3a 3a Electric charges q q 2q are placed at the corners of 22 an equilateral triangle ABC of side 1 The magnitude of electric dipole moment of the system is 1 ql 3 3ql 2 2q1 4 491 3 3a and 3a 1 ql 3 3ql ABC 19 9 2 face in and aga quia aftur 2 2q1 4 4ql

A particle revolving in a circular path completes first one third of circumference in 3 s while next one thin in 2 s The average angular velocity of the particle A rad s B Trad s 5 K rad s 15 C D 27 15 47 15 rad s

0 Consider the two statements related to circular motion in usual notations A In uniform circular motion and a are always mutually perpendicular B In non uniform circular motion v and a are always mutually perpendicular 1 Both A and B are true 2 4 Both A and B are false A is false but B is true

A particle is moving with constant speed v in xy plane as shown in figure The magnitude of its angular velocity about point O is ya 1 0 b of V a b vb 3 2 6 a 0 V 2 b 4 VIC X ON

In the shown arrangement particle at C connected by the help of two ideal strings is moving with minimum possible speed in form of conical pendulum as shown maintaining the configuration Find angular velocity of its revolution 0 2 m B 60 10 3 rad s 10 rad s 20 rad s 20 3 rad s C

Q6 A stone of mass is 1 kg tied 1 point to the end of a string of length 1 m whirled in horizontal circle with a uniform angular velocity of 2 rad s 1 The tension of the a 2N b string is 1 3N c 4 N d 1 4N O A B O C O D O Other

Q5 A car is moving along a horizontal curve of radius 20 m and coefficient of friction between the road and wheels of the car is 0 25 If acceleration due to gravity is 9 8 m s2 then its maximum speed is b 5 m s c 7 m s d 9 m s a 3 m s O A OB O C O D O Other 1 po

Topic Electrostatic from Suspended Ball System To problems based On Conservation of Mechanical Energy Gravitation From Gravitational Potential Energy to Problem Based On Kepler s Law A convex mirror of focal length f forms an image 1 and and are fafara R which is times the object The distance of the n real object from the mirror is 1 1 n 1 f n 1 1 f 2 a cri 1 n 1 f CTX n 1 n Ja arafa af 2 n IC

37 A charge having e m equal to 108 C kg and with velocity 3 x 105 m s enters into a uniform magnetic field B 0 3 tesla at an angle 30 with direction of field The radius curvature will be a 0 01 cm b 0 5 cm c 1 cm d 2 cm

which is accelerated downward Suppose a boy is enjoying a ride on a merry go round which is moving with a constant speed of 10 ms 1 It implies that the boy is a at rest b moving with no acceleration moving with uniform velocity c in accelerated motion Assertion Mass is a measure of inertia of the body in linear motion

A circular road of radius 1000 m has banking angle 45 The maximum safe speed of a car having mass 2000 kg will be if the coefficient of friction between tyre and road is 0 5 Question Type Single Correct Type 1 100 3 m s 2 124 m s 3 99 m s 4 86 m s

and m3 are connected to massless strings as shown on a frictionless table They are pulled with a force T3 40N If m m T 6kg and m3 4kg the tension T 2 will be 10kg m2 m T m3 T3

Railway tracks are banked at the curves so that ONO the train may not fall down inwards the weight of the train may be reduced the necessary centripetal force to train may be obtained from the horizontal compoinent of the reaction force of railway tracks no frictional force may be produced between the wheel