Circular Motion Questions and Answers

A particle A of mass m is attached to a vertical axis by two strings PA and QA of lengths 3L and 4L respectively PQ 5L A rotates around the axis with an angular speed 0 The tensions in the two strings are T and T 3 L 5 L 4 L i T T ii 37 4T 5 mg iii 47 37 12 mo L 2 1 i only 3 i iii A 2 i ii 4 ii iii CU

2 The around the world yo yo trick is completed when you twirl a yo yo in a vertical circle Assume the yo yo was in uniform circular motion Draw a free body diagram and write out the supporting net force equations Then compare the force of tension at the top of the circle to the force of tension at the bottom of the circle

radius 2m with a speed of 10m s Calculate the time after which the magnitude of change in its momentum becomes equal to its initial momentum L 1 T 15 sec 2 2 sec 15 75 3 se sec t

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road If the banking angle is 45 the speed of the car is Question Type Single Correct Type 120 ms 1 230 ms 1 3 5 ms 1

2 POTA HAJASTHAN Aparticle originally at rest at the highest point of a smooth sphere of radius R is slightly displaced If will leave the sphere at a vertical distance h below the highest point such that 1 h R 3 h R 2 h R 200R 1 2 h 3 4 h 2R 3 particle goes from point to point

A projectile is projected with velocity v at an angle 8 with horizontal The magnitude of radial acceleration of projectile is First decrease then increases First increase then decreases Always increases XRemains constant

Question No 1 Two particles A and B are initially at rest at the points R 0 and 0 R Starting at t 0 the particles move anti clockwise along the circular path of radius Rcentred at 3v the origin shown in the figure with constant speed vand The time instant when the particles meet for the first time is O O 7 3R 2mR Y r B 0 8 4 8 0 X

F2 R Wheel A F 9 B F 3 C F D 3F Axle R 3 0 F Note Vectors not drawn to scale 9 A wheel of radius R is fixed to an axle of radius R 3 and rotates at constant angular speed as shown in the figure above A force of magnitude F is applied tangent to the outer edge of the wheel A second force of magnitude F2 is applied tangent to the edge of the axle to keep the wheel rotating at constant angular speed The magnitude F is equal to

Q 22 A particle performing linear S H M with period 6 second is at the positive extreme position at t 0 The particle is found to be at a distance of 3 cm from this position at time t 7s before reaching the mean position Find the amplitude of S H M 0 23 Derive an expression to determine the speed of efflux through an orifice

A weightless thread can withstand tension upto 30 N A stone of mass 0 5 kg is tied to it and is revolved in a circular path of radius 2m in a vertical plane If g 10 m s then the maximum angular velocity of the stones can be 1 5 rad s 2 30 rad s 3 60 rad s 4 10 rad s

Acceleration of the three masses A B and C are shown in figure Friction coefficient between all surfaces is 0 5 Pulleys are smooth Given m 1kg m 1kg mc 2kg A ac C B 17g 22 7g 18 AO II B C B ac D a 7g 9 7g 18

The friction coefficient between the board and the floor shown in figure 6 E7 is ut Find the maximum force that the man can exert on the rope so that the board does not slip on the floor M

1 A simple pendulum consists of a 50 cm long string connected to a 100 g ball The ball is pulled aside so that the string makes an angle of 37 with the vertical and is then released Find the tension in the string when the bob is at its lowest position P

The stress strain curves are drawn for two different materials X and Y It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y We can say that materials X and Y are likely to be respectively a ductile and brittle b brittle and ductile c brittle and plastic d plastic and ductile 1 1 NEET 2015

Example 7 14 The angular speed of a rpm motor wheel is increased from 1200 to 3120 rpm in 16 seconds i What is its angular acceleration assuming the acceleration to be uniform ii How many revolutions does the engine make during this time W

The horizontal reaction force Rx that caused the horizontal acceleration ax in the figure below was m 70 kg 1 11 kg m Ax 3 2 m s Ay 12 9 m s 132 N O 155 N O 182 N 232 N 1 1 m None of the above 2m mg

4 20 If the ratio of time periods of circular motion of two charged particles in magnetic field is 1 2 then the ratio of their kinetic energies must be A 1 2 C 2 1 B 2 1 D It can have any value 4 21 Figure 4 220 shows a charged

14 Assertion A car moves along a road with uniform speed The path of car lies in vertical plane and is shown in figure The radius of curvature R of the path is same everywhere If the car does not loose contact with road at the highest point it can travel the shown path without loosing contact with road anywhere else Reason For car to loose contact with road the normal reaction between car and road should be zero Car TTTTT 50

A body of mass 10 kg is attached to a 30 cm long wire whose breaking stress is 4 8 x 107 N m The area of cross section of the wire is 106 m What is the maximum angular velocity with which it can be rotated in a horizontal circle

are attached respectively to the mid point and one end of a light string Another end of the string is kept fixed The masses are thrown to move on circular paths on a smooth honzontal table During the motion string remains straight The ratio of T and T as shown in figure is A T 2 3m 6

What is the ratio of the centripetal accelerations of the tip of the minute and hour hand of a clock if minute hand is 1 5 times longer than the hour hand 1 18 2 27 4 216 3154

ULAR MOTION 1 12A flat plate moves normally with a speed v towards a horizontal jet of water of uniform area of cross section The jet discharges water at the rate of volume V per second at a speed of V The density of water is p Assume that water splashes along the surface of the plate at right angles to the original motion The magnitude of the force acting on the plate due to the jet is

11 Three rods of identical geometry but different materials are welded to form the english alphabet letter Y as shown If their conductivity are K 2K and 3K and end temperature are 20 C 20 C and 100 C respectively then their junction temperature T is 20 C 100 3K 1 70 C 4 T K 2K map CON 20 C 2 60 C

1 m has mass 100 g and a speed of 1 4 m s at the lowest point in its path Find the tension in the string at this instant 15 Suppose the bob of the previous problem has a speed of 14 m s when the string makes an angle of 0 20 radian with the vertical Find the tension at this instant You can use cose 1 0 2 and sin0 0 for small 0 14

3 A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 36 km h Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn Tako g 10 m s 2

An object is projected from the ground with speed u at an angle 0 with the horizontal The radius of curvature of its trajectory at maximum height is R and at the point of projection is R The ratio is 1 cos 0 2 sin 0 3 4 sin 0 cose cos 0 R R

A particle of mass m moves with constant speed v on a circular path of radius r Fin magnitude of average force on it in half revolution

A car of mass m passes over a hump in a road that follows the arc of a circle of radius R as shown in the figure below a If the car travels at a speed v what force does the road exert on the car as the car passes the highest point of the hump Use any variable or symbol stated above along with the followi as necessary g n b What is the maximum speed the car can have without losing contact with the road as it passes this highest point Use any variable or symbol stated above along with the following as necessary g

A point object of mass m is kept at a 0 along x axis What mass should be kept at 3a 0 so that centre of mass lies at ongin 3 El 2 2m 4 3m

A 1 ms 2 B 2 ms2 C 0 5 ms 2 D 4 ms 2 A particle of mass m describes a circle of radius r The centripetal acceleration of the particle is 4 r2 What will be the momentum mass x velocity of the particle A 2m r B 2m r C 4m r D 4m r Two different masses are connected to two strings as shown in the figure Both masses rotate about a

derive Using the energy conservation the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity s zero speed possibl

2 One end of a light inextensible thread of length 1 is held stationary over a frictionless horizontal floor while a small bead tied at the other end of the thread is describing a circular path with a uniform speed vo on the floor as shown in the figure The upper end of the thread is suddenly pulled vertically upwards with a constant acceleration ao If the bead does not leave the floor find magnitude of its acceleration immediately after the upper end of the thread is pulled

A particle is moving with speed v on a circle of radius r and centered at origin as shown in the given figure in anticlockwise fashion Average acceleration of the particle during its motion from point A to point B is Y V Doubl 1 2v 1 1 Tur B A X 2 2 i j Tr

23 A cylindrical object of outer diameter 10 cm heigh 20 cm and density 8000 kg m is supported by a vertical spring and is half dipped in water as shown in figure 13 E6 a Find the elongation of the spring equilibrium condition b If the object is slight depressed and released find the time period of resulting oscillations of the object The spring constant 500 Nm eeeeee

shows four situations with a small ball of mass m connected to an ideal string of length I and fastened to a point O whose acceleration if any is shown in the diagram Column 11 lists the minimum value of speed u when the string is vertical in order for the mass to complete the circular motion in vertical plane Column III lists the maximum tension throughout the circular motion corresponding to minimum speed 1 II III IV 19 3 l l l 3 u 2g 1 28e 3 1 iii 5 ge iv 20 gl 3 Column 3 P 6 mg Q 4 3 mg R 7 mg S 8 mg

10 A block is tied with a thread of length and moved in a horizontal circle on a rough table Coefficient of friction between block and table is 0 2 Find tan 0 where 0 is the angle between acceleration and frictional force at the instant when speed of particle is v 1 6lg Apetit 0 2

C RBV and Q is at higher potentia SECTION D CIRCUIT PROBLEMS WITH DYNAMICS 6 A axis as shown A uniform magnetic field B exists in a horizontal plane The disc is connected with the The block of mass M is connected by thread which is wound on a pulley free to rotate about fixed horizontal resistance R as shown Calculate the terminal velocity of the block if it was released from rest Treat pulley as uniform metallic disc of radius L 4mgR B L B 3mgR 4B L X X X X X X X X X X X R X Xxx X X X X X M X X X X X X X X X X X X X X XX C 2mgR B L D 3mgR 28 L

A hoop of radius r and mass m rotating with an angular velocity is placed on a rough horizontal surface The initial velocity of the centre of the hoop is zero What will be the velocity of the centre of the hoop when it ceases to slip 2013 1 roo 3 3 roo 2 4 rwo 2 roo 4

D None of these The second s hand of a watch has 6 cm length The speed of its tip and magnitude of difference in veloc of its at any two perpendicular positions will be respectively A 2n 0 mm s C 2 2 T 2 mm s B 2 2 4 44 mm s T D 2n 2 2 mm s

A resistor R and 2 F capacitor in series is connected through a switch to 200 V direct supply Across the capacitor is a neon bulb that lights up at 120 V Calculate the value of R to make the bulb light up 5 s after the switch has been closed log 0 2 5 0 4 2011 2 2 7 1062 4 1 3 10452 1 2 3 10752 3 3 3 107

A circular disc X of radius R is made from an iron plate of thickness t and another disc Y c radius 4R is made from an iron plate of thickness 14 Then the relation between the moment 200 inertia Ix and ly is 1 ly 321x 3 ly 32 lx 2 ly 161x 4 ly 64 Ix

A particle of mass m connected to a string of length 7 which is rotating in a vertical circle such that the ratio of the maximum to the minimum tension in the string is 2 1 then find out the speed of the particle at the bottom most point 1 13gl 3 11g 2 12g 4 10g

A particle is moving on a circular path with continuously decreasing speed The correct relation is where symbols have their usual meanings 1 V 0 3 F V 0 2 a v 0 4 All of these

28 A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity to in a circular path of radius R figure 7 E3 A smooth groove AB of length L R is made on the surface of the table The groove makes an angle 0 with the radius OA of the circle in which the cabin rotates A small particle is kept at the point A in the groove and is released to move along AB Find the time taken by the particle to reach the point B R B

56 A body crosses the topmost point of a vertical cird 7 with critical speed What will be its centripet when the string is horizontal acceleration 1 g 3 3g 2 2g 4 6g

A motorcyclist is maintaining constant speed while going on an overbridge of radius R When the motorcycle is ascending on the overbridge the normal reaction on it 1 Increases 2 Remains same 3 Decreases 4 Initially increases upto 45 with vertical and then decreases

6 Stone tied at one end of light string is whirled round a vertical circle If the difference between the maximum and minimum tension experienced by the string 3 kg wt then the mass of the stone must be 1 1 kg 2 kg 3 2 kg 4 4 kg

A bucket full of water is tied with the help of a 2 m long string The minimum angular velocity of bucket at the uppermost point so that water will not fall is 1 2 5 rad s 3 5 rad s 2 5 rad s 4 10 rad s

An unbanked curve has a radius of 60 m Coefficient of friction between the tyre of truck and road is 0 75 The distance between two front wheel of truck is 2 m If the truck exceeds the speed of safe limit then their 1 Inner wheels leave the ground first 2 Outer wheels leave the ground first

A block of mass m is kept on horizontal turn table at x distance from the centre If coefficient of friction betwe block and surface of turn table is u then maximum angular speed of the table so that block does not slip W 5 ug 2x 0 X 0 2 4 m ug V x 2 MX state