Circular Motion Questions and Answers

15 A particle is moving in a circular orbit with constant speed Select wrong alternate Its linear momentum is conserved b Its angular momentum is conserved c It is moving with variable velocity It is moving with variable acceleration 7 5X2 X0 0 70 6

acceleration a He swings a stone tied to a string of length in a vertical plane The string remains stretched throughout the time of rotation g is acceleration due to gravity Then answer the following Read Less What is the minimal velocity VA at the point A needed to keep the string stretched throughout the circular path 0

33 A satellite is moving in a circular orbit round the earth with a diameter of 2R At a certain point a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially The resulting orbit of the satellite would be a same as before b circular orbit with diameter greater than R c elliptical orbit with minimum distance from the centre of earth equal to R d elliptical orbit with maximum distance from the centre of earth equal to R

3 90 4 27 A block of mass m is kept on horizontal turn table at x distance from the centre I block and surface of turn table is u then maximum angular speed of the table so that block does not slip 2 ug LLX

R 2 11 A circular rope of weight W and radius r is resting on a smooth sphere of radius R The tension in rope is A C W T 6 W T 10 rope W 12 D None of these a B A E 8 3 C

Which of the following statements is false for a particle moving in a circle with a constant angular speed 1 The velocity vector is tangent to the circle 2 The acceleration vector is tangent to the circle 3 The acceleration vector points to the centre of the circle 4 The velocity and acceleration vectors are perpendicular to each other

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal Each of the rotation axes passes through the centre of the square Then the ratio of angular speeds 0 02 03 is WB JEEM 2014 A 1 1 1 1 C 1 2 1 2 B D 3 2 2 1 1 2 2 Hy

Problem 4 5 The equal masses in the figure oscillate in the vertical direction Show that the frequencies of the normal modes of oscillation are given by w 3 5 2 m and that in the slower mode the ratio of the amplitude of the upper mass to that of the lower mass is 5 1 whilst in the faster mode this ratio is 5 1

ms 32 The velocity of a body moving in a vertical circle of radius r is 7gr at the lowest point of the circle What is the ratio of maximum and minimum tension a 4 1 c 3 1 b 7 1 d 2 1

A toy truck weighing 7 kg travels at a constant speed of 8 m s around a circular track The diameter of the circular track is 90 m What is the magnitude of the centripetal force of the truck Please write the answer in one decimal place e g 1 234 should be w 1 2

3 1 1 A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km hr The centripetal force is 1 1000 N 3 250 N 2 750 N 4 1200 N m s moving in a circular path having radius R and r If their

A metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own in such a way that each part of the ring moves with a speed v Tension in the ring is mv my 1 2 R R 4 Zero 2 3 2 my 2R

Find magnitude of average acceleration between the points P and Q for a particle performing uniform circular motion Radius of circle is 2 m 4m s 1 3 84 11 m s 84 m s 22 Q 60 4m s P 2 no 1A m 4 82 11 82 22 m s m s

A ceiling fan rotates about its own axis with some angular velocity When the fan is switched th off the angular velocity becomes of the original in time t and n revolutions are made in that time The number of revolutions made by the fan during the time interval between switch off and rest are Angular retardation is uniform 4n 8n A 15 B 15 C 16n 15 D 32n 15

whaco A disc rotates about a fixed axis Its angular velocity a varies with time according to the equation at b Initially at t 0 its angular velocity is 1 0 rad s and angular position is 2 rad at the instant t 2 s angular velocity is 5 0 rad s Determine angular position 0 and angular acceleration a when t 4 s elxs ne

An experimenter two trigger simultaneously producing a big flash located at the origin of his reference frame and a small flash at x 30 0 km An observer moving at a speed of 0 250 c in the positive direction of x also views the flashes What is the time interval between them according to him a 25 8 s c 75 0 s arranges to flashbulbs b 51 6 s d 100 s

A particle of mass m is moving in circular path of constant radius r such that centripetal acceleration is varying with time t as K rt where K is a constant The power delivered to the particle by the force acting on it is A m K B mk r t C m K rt D m Krt

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km h 1 The centripetal force is 1 250 N 2 750 N 3 1000 N 4 1200 N

Example 14 10 For a CE transistor amplifier the audio signal voltage across the collector resistance of 2 0 k2 is 2 0 V Suppose the current amplification factor of the transistor is 100 What should be the value of R in series with VBB supply of 2 0 V if the de base current has to be 10 times the signal current Also calculate the de drop across the collector resistance Refer to Fig 14 33

Q No 43 For the given situation find tension T at point P in string Particle is moving in vertical circular motion 1 2 3 4 Correct Answer 2 Complete Question Content 50 N 66 N 70 N None of those t Im 10m s 1 kg

The adjoining diagram shows the electric lines of force emerging from a charged body If the electric fields at A and B are E and EB respectively and the distance between them is r then 1 EA EB 3 EA EB A B 2 EA EB A B 4 EA EB 2

a m s 6 6 Figure gives the acceleration of a 2 0 kg body as it moves from rest along x axis while a variable force Om to x 9m The work done by the force on the body when it reaches acts on it from x i x 4m and ii x 7 m shall be as given below 2 78 4 INI 1 21 J and 33 J respectively 2 21 J and 15 J respectively 3 42 J and 60 J respectively 4 42 J and 30 J respectively x m

4 An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction B If kinetic energy is doubled and magnetic induction tripled the radius will become 3R d R a 2 b 3 R R

21 A wheel is subjected to uniform angular acceleration about its axis Initially its angular velocity is zero In the first 2 s it rotates through an angle 0 in the next 2012 s it rotates through an angle 02 The ratio of 19 a 1 c 3 b 2 0 2 is 0 1 d 5 hout its axis with

S I A student skates up a ramp that makes an angle 30 with the horizontal He she starts as show figure at the bottom of the ramp with speed vo and wants to turn around over a semicircular path radius R during which he she reaches a maximum height h at point y from the ground as shown figure Assume that the energy loss is negligible and the force required for this turn at the highes is provided by his her weight only Then g is the acceleration due to gravity A v 2gh gR 3 B v 2gh gR 2 C the centripetal force required at points x and z is zero D the centripetal force required is maximum at points x and z A D Speed at x and z is equal and also maximum in circular track From Energy conservation 1 2 1 mv mgh mv 2 1 2 at y mgsin30 v 2g 2 mv R From equation 1 30 Rg 2 v 2gh R x

A block of mass m is tied to a string of length L and the assembly is kept on a smooth horizontal table as shown in the figure Now the other end of the string is moved with a constant velocity vo j xy plane is the plane of the table Then A m will execute an oscillatory motion B m will follow a circular path as seen fro the ground C Angular momentum of m will remain conserved about the other end D Angular momentum of m will remain conserved about the origin

A blcok of mass M is situated on a smooth the block passes through a hole in the table and carries a mass m at its other end if the length of the thread above the table is I what should be the value of m so that it may remain suspended at a constant height and the block M moves in a circular path with an angular velocity w on the table M

A particle starts from rest and performing circular motion of constant radius with speed given by v a where a is a constant and x is the distance covered The correct graph of magnitude of its tangential acceleration a and centripetal acceleration a versus t will be 84 E DNN a

The vapour pressure of pure benzene and toluene are 160 and 60 torr respectively The mole fraction of toluene in vapour phase in contact with equimolar solution of benzene and toluene is 1 0 50 2 0 6 3 0 27 4 0 73

A vertical spring of length lo and force constant kis stretched by a when a mass m is suspended from its lower end By pulling the mass down a little the system is left off to oscillate The time period of oscillation is 2 T O271 O 2T 2

36 A frame is rotating in a circle with varying speec v 2t 4 m s where t is in second An object is viewed from this frame The pseudo force a is maximum at 2 s b is minimum at 2 s c is zero at 2 s d Data is insufficient

Question 3 A wheel which is initially at rest is subjected to a constant angular acceleration about its axis It rotates through an angle of 15 in time t sec The increase in angle through which it rotates in the next 2t sec is

53 Two particles A and B are moving with equal speed V but in opposite direction such that distance between them remains constant which is D After how much time A will reach the initial position a C 2D V 2TD V b TD V d D 2V

2 Kevin is riding a Ferris wheel From the starting point at the very bottom he reaches the top of the Ferris wheel which is 20m high in 16 seconds Assume the Ferris wheel s rotation speed is constant b What is the radius of the wheel 1

6 Assertion When an automobile while going too fast around a curve overturns its inner wheels leave the ground first Reason For a safe turn the velocity of automobile should be less than the value of safe limit velocity

A particle of mass m is fastened to one end of a string and one of m to the middle point the other end of the string being fastened to a fixed point on a smooth horizontal table The particles are then projected so that the two portions of the string are always in the same straight line and describes horizontal circles Find the ratio of tensions in the two parts of the string

In figure the bob of a conical pendulum of length and weight W describes a horizontal circle defined by the equations x acosot y a sin oot where a is the radius of the circular path and to is a constant The tension in the string is W a xloo 2g W b x10 g W c g xa d W

When a mass goes in a horizontal circle with speed v at the end of a string of ength L on a frictionless table the tension in he string is 6N If the speed of this mass vere doubled but all else remained the ame the tension would be r T m

m volume cylinder is filled with 1 mole of 0 gas at room temperature 300 K The molecular diameter of O and its root mean square speed are found to be 0 3 nm and 200 m s respectively What is the average collision rate per second for an 0 molecule a 10 0 b 10 c 10 2019 Main 10 April 1 d 10 3

Two parallel disks have diameters of 50 cm and are separated by a distance of 12 5 cm One disk is maintained at a constant temperature of 600 C and has 0 63 while the other generates a constant heat flux of 80 kW m and has e 0 75 The disks are surrounded by a large room at 30 C Calculate the heat absorbed by the room and the temperature of the constant heat flux disk

I wo beads each of ma m are positioned at top of a frictionless hoop of mass M and radius R which stands vertically on ground The beads are pushed gently so that they slide down the hoop One to the right and one to the left If during subsequent motion hoop is to loose contact from ground then minimum value of is a Find m M 4a Sr Super60 All R mm 777 Space for rough work 7 22 Page 6

haitanya IIT Academy 17 06 2021 Sr Super60 All Jee Adv 2019 P2 GTA 10 A particle is moving x y plane At certain instant the components of its velocity ar acceleration are as follows

formation 19 Two identical small beads A and B threaded on an almost inertia less horizontal rod of length 21 are connected by a light inextensible cord of length 1 21 Initially the beads are adjusted equidistant from the centre of the rod and the rod is rotating about its central vertical axis at an angular velocity 1 3 rad s At some point of time the cord is cut and the beads begin to slide on the rod without friction Neglect effects of gravity Which of the following statements are correct Path of a bead in an inertial frame is a spiral b Path of a bead in an inertial frame is a straight line c To leave the rod the beads take 4 s after the cord is cut d To leave the rod the beads take more than 4 s after the cord is cut 2B BC

0 A uniform rod of mass M 2kg and length L is suspended by two smooth hinges 1 and 2 as shown in figure A force F 4N is applied downward at a distance L 4 from hinge 2 Due to the application of force F hinge 2 breaks At this instant applied force F is also removed The rod starts to rotate downward about hinge 1 g 10m s 05 1 The acceleration of the end point of the rod of small mas dm at the end point of the rod when the rod becomes vertical is B 30m s 20m s 2 Your Answer L

A thin uniform metallic triangular sheet of mass M has sides AB BC L What is its moment of inertia about axis AC lying in plane of sheet M 12 ML JIN A B 45 VIN 452 2ML L usc ML ML

A cavity is to be designed to serve as a blackbody source The proposed shape is that of a truncated conical hole with an opening of 25 mm and diameter at the bottom of 6 mm If the surface emissivity of the cavity is 0 9 estimate the cavity depth necessary to produce an apparent emissivity of 0 98

below on the left It is on a horizontal floor and a meter scale is positioned horizont on its axle with one edge of the scale on top of the axle see figure on the right The scale is now pushed slowly on the axle so that it moves without slipping on the axle and the roller starts rolling without slipping After the roller has moved 50 cm the position of the scale will look like figures are schematic and not drawn to scale C a b c d x 0 x 50 cm 75 cm x 0 x 25 cm x 0 x 100 cm

more as egg 2 Assertion The spokes near the top of a rolling bicycle wheel are more blurred than those near the bottom of the wheel Reason The spokes near the top of wheel moves faster than those near the bottom of the wheel

The orbital speed and the orbital radius of a satellite moving around a planet of mass 4 68 1023 kg are 3759 m s and 6 25 108 m Determine the orbital radius of the second satellite if its orbital speed is 5346 m s a 1 57 108 m b 2 17 108 m c 4 39 108 m d 3 09 10

Ex 3 A heavy bead slides on a smooth fixed circular wire of radius a Ifit is projected from the lowest point with a velocity just sufficient to carry it to the highest point prove that the radius through the bead in time t will turn through an angle 2 tan sinh t and the bead never reach the a