Kinematics Questions and Answers

The angle of elevation of an incline plane is A particle is projected up an incline plane with angle of projection with incline surface equal to The particle strikes incline plane normally Find value of coseco

The angle of elevation of an incline plane ise A particle is projected up an incline plane with angle of projection with incline surfo equal to e The particle strikes incline plane normally Find value of cos eco

Cute R M 4 coto 4 bard A rod of mass m and length is moving between perpendicular smooth walls as shown When roc is at angle 0 with horizontal its end B is moving right with speed v The speed of end A is YA S A ytanA B X 2 v cote

agraph for Question Nos 8 to 10 A physics tutor launches a home built model rocket straight up into the air At t 0 the rocket with V t 0 0 The acceleration of the rocket is given by g ag Bt4 0 t t where t ag B 1 4 ay g t tb is the time at which fuel burns out a is a positive dimensionless numbe ll timor in the interyal 0 t t is

4 4 2 6 8 t sec I Acceleration of an object is zero at time t 4 s II The net displacement of the body is zero in the given graph SolveLancer Test a I is incorrect and II is correct b I is correct and II is incorrect c Both statements are correct d Both statements are incorrect

The equation of trajectory of a particle projected from the surface of the planet is given by th equation y x R d Then match the columns suppose g 2 m s Column I A angle of projection tan 233 tan 9 B time of flight T C maximum height attained H D horizontal range R Column II magnitude only p 1 4 q 1 r 2 s 4

A block with mass M lies on a slippery horizontal surface On top of it there is another block with mass m which in turn is attached to an identical block by a string The string has been pulled across a pulley situated at the corner of the big block and the second small block is hanging vertically Initially the system is held at rest Find the acceleration of the big block immediately after the system is released You may neglect friction as well as masses of the string and the pulley Take m 1kg M 2kg m M m

Full Marks Zero Marks O Negative Marks 1 If wrong option is selected Find moment of inertia about axis OA me 6 4 If correct answer is selected 0 If none of the option is selected me 6 n n 1 2n 1 zero me n n 1 2 O 10 m m 20 m 3

A particle can travel from point A to B from two different path 1 and 2 as shown in same interval of time Then which of the following is incorrect D A Average velocity along the two paths A and B are equal the particle may travel along both the paths without acceleration the direction instantaneous velocity along the path 1 and 2 can be same for a maximum of two point on the paths along path 1 the average and instantaneous velocity can have same direction at some instant

A long horizontal belt is moving from left to right with a uniform speed 2m s There are two ink marks A and B on the belt 60m apart An insect runs on the belt to and fro between A and B such that its speed relative to belt is constant and equals 4m s When the insect is moving on the belt in the direction of motion of the belt

38 The speed of an object undergoing uniform circular motion is 4 m s The magnitude of the change in the velocit RO during 0 5 see is also 4 m s Find the minimum possible centripetal acceleration in m s2 of the object Take z 25 8

A particle moves in a straight line from point A to point B The acceleration is given as a 5 2x m s2 where x is distance covered from point A in metres Particle start from rest and comes to rest at B Then A Maximum speed of particle is 5 2 m s 5 B Maximum speed of particle is 2 C Distance between A and B is 5 m D Distance between A and B is 10 m A B m s C

92 A particle of mass m is attached to three identical springs A B and C each of force constant k as shown in figure If the particle of mass m is pushed slightly against the spring A to releasedy then the time fariod of scillation A 2 m 2 k B

Four balls A B C and D are placed on a smooth horizontal surface Ball B collides with ball C with an initial velocity u as shown figure If all collisions are elastic find the total number of collisions between the balls A m B m C 2m D 2m

A man wants to cross a river along line AB flowing with speed 15 m s and whose width is 600m If the speed of man with respect to river is 20 m s Then B L 53 A A angle at which he should swim with respect to line AB is 30 B angle at which he should swim with respect to line AB is 45 c time taken by the man to cross the river is 30 sec D time taken by the man to cross the river is 60 sec 600m

A mass M is attached to a horizontal spring of force constant k fixed one side to a rigid support as shown in figure The mass oscillates on a frictionless surface with time period T and amplitude A When the k i ed 2 vig k a 189 York OF U M m MA M A mass M is in equilibrium position another mass m is gently placed on it What will be the new amplitude of oscillations mooooo ATHE m M b ag mmmmm d 45 90 rellllll M m M A m A M M m leeeeeee A from

Two buildings are 80 metres away and of height 75 m and 135 m A particle is projected from the lower building at 50 m per second making an angle of 53 towards other building from horizontal from the top of higher building another particle is horizontally projected at same time find if they can collide also find velocity for horizontal projection

An object of mass 4 kg falls from rest through a vertical distance of 10 m and reaches ground with a speed of 14 m s How much work is done against air friction in joules g 10 m s

A boy tosses a ball from a window that is 8 0 m above the ground When the ball leaves boy s hand it is moving at a speed of 10 0 m s at an angle of 20 below the horizontal When the ball hits the ground its horizontal distance from the window is A 12 2 m C 10 0 m B 7 4 m D 9 2 m

12 In the diagram shown the platform always remains horizontal The drums are rotating with angular velocities and 02 If the drums have the same radius R then find out the velocity of the platform A R 1 2 3 B R 001 002 12 C R 01 2 6 D None 02

Two people push a car of mass 1200 kg but the car doesn t mov e Three people push the same c ar and bring it to motion with a c onstant acceleration of 0 2 m s2 Find the force of Friction appli ed on the car

2 A body starting from rest accelerates uniformly at the rate of 10 cm s and retards uniformly at the rate of 20 cm s Find the least time in which it can complete a journey of 5 km if the maximum velocity attained by the body is 72 km h 1 400 sec 2 500 sec

A particle moves along a straight line with equation of motion s f t where s is measured in meters and t in seconds Find the velocity and the speed when t 2 velocity speed f t 18 24 t 1 m s m s

Here at t 2 seconds the velocity of the body is zero as it t ouches the axis so why can t we take acceleration as zero U V1 Average acceleration v m s 154 From the velocity time graph of a particle given in figure 3 W1 describe the motion of the particle qualitatively in the interval 0 to 4 s Find a the distance travelled during first two seconds b during the time 2s to 4 s c during the time 0 to 4 s d displacement during 0 to 4 s e acceleration at t 1 2 s and f acceleration at t 2 s Smey 10 5 0 5 10 1 N 20 m s m S t s

b The velocity of a body is given by v t 2t 1st 5 5t 3 5 t 14 Where is given in seconds and is given in m s Use the two segment trapezo rule to find the distance in meters covered by the body from 12 to 1 9 second

4 Two stones are projected with the same speed but making different angles with the horizontal Their ranges are equal If TC the angle of projection of one is and its 3 maximum height is y then the maximum height of the other will be

A ball rolls down a tube that is inclined at an angle of 53 with the horizontal The ball leaves the lower opening of the tube with a speed of 5 m s A strong horizontal wind imparts the ball uniform horizontal acceleration everywhere during its flight as shown in the figure As a result the ball strikes the ground at a point that is 12 m vertically below the lower opening of the tube What is the horizontal acceleration imparted by wind to the ball 53 5 m s 111 1 1 wind

d1 5 60 1 30 8 30k 2 2 00 4 00 2 00k d 3 2 00 3 00 1 00k a What results from a d d 3 b d a 3 and a a 3 c d and e for and 1 2 components respectively a Number b Number i c Number Units Units Units

A point charge q is fixed at point A on the circumference of a fixed smooth non conducting circular wire of radius R in a gravity free space A small ring of mass m and charge q which can slide freely on the wire track is given tangential velocity at point B which is diametrically opposite to A If the distance of closest approach between the fixed charge and the ring is R then force applied by the wire track on the ring just after the release will be F 3 3F 4 5F 4 2 1 q 4 o R 2 F 4 4 F

A body covers one third of the distance with speed v For the remaining distance it travels for half of the time with speed v another half of the time with speed v3 If average speed nV V2 V3 is 4v x y Find n

A particle moves in a circle of radius 1 m wit speed of 1 m s After completing quater cycle Find out i Displacement ii Distance travelled iii Average velocity is Av leration

A source emitting sound frequency 1000 Hz moves anticlockwise in the x y plane along the circle x 5 2 y 9 with a constant speed of 10 m s where x and y are in meters A stationary observer i located at the origin The speed of the sound in air is 330 m s 0 X coordinate of the source is 16 5 if frequency heard by the observer is maximum Y coordinate of the source is 12 5 if frequency heard by the observer is maximum X coordinate of the source is 16 5 if frequency heard by the observer is minimum

In a car race sound signals emitted by the two cars are detected by the detector on the straight track at the end point of the race Frequency observed are 330 Hz and 360 Hz and the original frequency is 300 Hz of both cars Race ends with the separation of 100 m between the cars Assume both cars move with constant velocity and velocity of sound is 330 m s Find the time in s taken by winning car 1

5 Assertion Motion with uniform velocity is always along a straight line path Reason In a motion with uniform velocity speed is the magnitude of the velocity and is equal to the instantaneous velocity I

A charged particle of charge q and mass m is released in an electric field of constant magnitude E The KE gained by particle after t seconds is 9 Et 2m O 2E2 2 9 m m O E 212 2m 92E21 2

A body of mass M is thrown vertically upward with some velocity It reaches to some height and returns to ground after some time The total change in momentum taking place is 6 Mg kg m s Total time of flight of the body is g is acceleration due to gravity 1 10 s 3 3 s 2 6 s 4 20 sep

Question 1 1 point An object is thrown with a speed of 11 2 m s at an angle of 52 6 degrees above the horizontal What is the maximum height in metres that it rises to Give your answer with 2 digits precision Your Answer

A particle moving along a straight line has a velocity v m s when it cleared a distance y metre These two are connected by the relation v 49 y When its velocity is 1 m s its acceleration in m s is O 1 2 O 7

The acceleration time graph ing along straight line is as shown in the figure What is the velocity of the particle at t 8 sec if initial velocity of particle is 3 m s a m s 4 1 4 m s 2 5 m s 3 1 m s 0 1 4 8 t s

Three forces of 4N IN and 2N acting on a body are as shown in the figure We want to have the resultant force only along the y direction What should be the magnitude of the minimum additional force required for it ya O 4 N 0 5 N 30 60 IN X 2N

an object is dropped from a top of a building of 100 M height at the same moment another object is thrown with some initial velocity from the ground so that it just reaches at the top of the building then find the time after which two objec meet each other and the positions where they meet each other 1 51 PM

xplain each step property 6 Figure shows a graph of position versus time graph for a particle moving along x axis Straight line Parabola Column I A Slowing down B Returning towards origin C Moving away from origin D Speeding up Parabola Column II P t R t t S t t t t A A P S T B R C P S D Q R B A R B P S T C Q R D P S C A P S B R C Q S D S T D A QR B P S C R S T D Q R T Straight line Parabola

The initial velocity of a particle is 41 31 m s It is moving with uniform acceleration u 0 41 0 31 m s What is the magnitude of its velocity after 10 s a O O O 8 m s 4 m s 6 m s 10 m s

A force given by F x 5x x in N m acts on a 1 00 kg mass moving on a frictionless surface The mass moves from x 2 00 m to x 6 00 m a How much work is done by the force b If the mass has a speed of 2 00 m s at x 2 00 m what is its speed at x 6 00 m

a police Jeep is running behind motorbike the motorbike process a turning at the speed of 20 ms while the Sheep follows it at a speed of 30ms the bike process are turning 10 second before the Jeep the catch is after t seconds find how far from turning will the Jeep catch the bike 1 49 PM

Velocity of a swimmer with respect to a river is 45 m s and velocity of the river flow is 21 m s then velocity of swimmer with respect to ground is in m s A 2j C i 6j B 1 21 D None of these

A ball is thrown vertically upwards with a velocity u with respect to ground from the balloon descending with velocity V The ball will pass by the balloon after time A C u V 2g 2 u V g B D u V 2g 2 u V g

variable acceleration Variation of square root of speed of a particle moving on the x axis is as shown Its initial magnitude of acceleration is v 3 60 A 2 3 m s C 6 3 m s to B 3 3 m s D 8 3 m s t

Q 68 In ideal gas is enclosed in an adiabatic container having cross section A 27 cm for a part of it up by www k 3H 32 A 2 and for remaining part Pistons 2 P and P can move freely without friction along the inner wall In the position shown in the figure the spring attached to the piston P is relaxed Sprig constant the spring is K 3700 N m Piston P is pushed up gradually through 2 H a distance and its was observed that the piston P goes 2 Take y 1 5 mass of piston P 13 5 kg and H 2 A H atmospheric pressure P 1 x 105 N m a Find H b Find final temperature of the gas if its initial tem 200 IZ

Q76 Two racing cars of masses m and m are moving in circles of radii r and r respectively Their speeds are such that each makes a complete circle in the same time t The ratio of the angular speeds of the first to the second car is a 1 1 c r r b m m d m m r r