Work, power & energy Questions and Answers

e A simple pendulum has a mass 3 4 kg and a length 2 35 meters If the mass is released from rest at an angle 62 8 degrees how much velocity in m s will the mass have when it reaches the bottom of its path

31 A block attached to a spring pulled by a const horizontal force is kept on a smooth surface as shown in the figure Initially the spring is in the natural state Then the maximum positive work that the applied force F can do is Given that spring does not break F k 15 a k ooooooo b F 2F2 k 2

29 In the figure a block slides along a track from one level higher level by moving through an intermediate valley The track is frictionless untill the block reaches the higher level There a frictional force stops the block in a distance d The block s initial speed v is 6 m s the height difference h is 1 1 m and the coefficient of kinetic friction u is 0 6 The value of d is 0 to a a 1 17 m 7 0 b 1 71 m d 11 0 6 Th 34 W a 35 3

2 A 10 gm bullet is fired into a 990 gm black rest on a horizontal frictionless surface The block with the bullet embedded in it slides up an inclined frictionless surface and stops The initial speed of the bullet is v a Find the speed of the block just after the bullet strikes it b Find the rise in height H of the block BEFORE AFTER 302 H

Two electrical bulbs marked 40 W 220 V and 60 W 220V when connected in series across same voltage supply of 220 V the effective power is P and when connected in parallel the effective power is P2 Then P P2 is Question Type Single Correct Type 1 0 5 2 0 48 3 0 24

rrect answer Type Questions A constant force F acts on a moving body along a smooth quater circular arc of radius R fixed on horizontal surface Calculate the work done by force F from A to B B a If force F always points towards B then work F 2R FRA 2 b If force F always acts tangentially 2 c If force F always acts parallel to AB F 2R d If force F always acts parallel to AB Zero 16 A 0 1 kg block is pressed against a horizontal spring fixed at one end to compress the spring through 5 cm The spring constant is 100 Nm The ground is 2 metre below the spring Which of the following pra tant Falco 10

Answer the following questions orally 1 If we press a sheaf of paper very hard with our thumb it may crease a bit but otherwise we do not see any change However if we press it with a sharp pin we can make a hole in it Why is this so

0 A particle is thrown up vertically with a speed in air It takes time t in upward journey and t t in the downward journey and returns to the starting point with a speed v Then 2 V V 1 V V 3 V V d idpism 4 Data is insufficient 0103 KINEMATICS 03 EXERCIS

41 A block of mass M moving with a velocity vo on a horizontal table strikes a spring of spring constant k at t 0 and begins to experience a frictional force The co efficient of friction is variable and is given by bx where x is the compression in the spring The loss in mechanical energy when the block first comes momentarily to rest is gbMv2 2k gbMv2 a c Vo M k voooooo b d Mgbv 2 k gb M gbv2 2 k Mab

k 32 A man is supplying a constant power of 500 J s to massless string by pulling it at a constant speed of 10 m s as shown It is known that kinetic energy of the block is increasing at a rate of 100 J s Then the mass of the block is J a 5 kg c 10 kg 60 m b 3 kg d 4 kg

2 Assertion The work done by the radial force acting on a particle when doing uniform circular motion is zero Reason No work is done by a force if force is perpendicular to the elementary displacement

c 10 kg 33 In the figure shown all the surfaces are frictionless and mass of the block m 1 kg The block and wedge are held initially at rest Now wedge is given a horizontal acceleration of 10 m s2 by applying a force on the wedge so that the block does not slip on the wedge Then work done by the normal force in ground frame on the block in 3 s is 10 m s a 100 J c 150 J m b 200 J d 100 G

Incline planes P Q are smooth but plane surface from A to B is rough Find number of times block of mass 2 kg will climb on Q If released from P at a height 50 m a 45 c 42 b 41 d 40 P A H 0 2 3m B H 50m

10 A block is released from the top of two inclined rough surfaces of height h each The angle of inclination of the two planes are 30 and 60 respectively All other factors e g coefficient of friction mass of block etc are same in both the cases Let K and K be the kinetic energies of the block at the bottom of the plane in two cases Then a K K c K K 00 400 b K K d Data insufficient

5 A cyclic process is shown in the figure Work the cyclic process ABCDA A 2 10 10 a 150 J b 163 J D C B 2 3 V c 145 J d 166 J

9 A vertical spring of force constant 100 N m is attached with a hanging mass of 10 kg Now an external force is applied on the mass so that the spring is stretched by additional 2m The work done by the force Fis g 10 m s a 200 J b 400 J c 450 J origh k 100N 110kg F d 600 J

5 A body is displaced from 0 0 to 1m 1m along the path x y by a force F x j yi N The work done by this force will be 4 a J c 13310 2 STONT b J d 715

A particle of mass 4 kg is at rest at position A 2 3 If it is moved to point B 3 5 by applying a constant force F 41 61 3k N If speed of particle at B is co ordinates are in metre N N m s then value of N is

3 A particle falls from rest under gravity Its potential energy PE with respect to ground and its kinetic energy KE are plotted with time t Choose the correct graph 1 3 E PE E PE KE t KE 2 4 E PE E KE PE KE

2 A stone of mass 10 g is dropped from the top of a tower of height 1 km It falls under gravity in presence of air resistance Air resistance is directly proportional to speed of stone and the stone hits the ground with speed 50 m s The work done by air resistance In J is equal to

By applying a force F 3xy 5z j 4zk particle is moved along the path y x where all quantities are in SI units from point 0 0 0 m to the point 2 4 0 m The work done by force F on the particle in joule is y y x 2 4 0

1 A thin rod of length L and mass M is held vertically with one end on the floor and is allowed to fall What will be the angular velocity of the other end when it hits the floor assuming that the end hits on the floor a 3g VI L rad b 3g L

A playground merry go round of radius R 1 80 m has a moment of inertia I 270 kg m and is rotating at 8 0 rev min about a frictionless vertical axle Facing the axle a 23 0 kg child hops onto the merry go round and manages to sit down on the edge What is the new angular speed of the merry go round Trex min

Fr where Fis a positive constant and is its distance from the origin Its energies are calculated using the Bohr model If the radius of the particle s orbit is denoted by Rand its speed and energy are denoted by vand E respectively then for the orbit here is the Planck s constant a R 1 8 and von b R n and von c E 3 n h F 2 4 m d E 2 n h F 4x m

The position x of a particle of mass 2 kg moving along x axis at time t is given by x 2 metre Find the work done by force acting on it in time interval t 0 to t 2s 1 576 J 3 623 I 2 584 J 4 None

6 A ball collides perfectly inelastically with smooth horizontal ground at angle 30 with vertical as shown Fraction of kinetic energy lost by the ball due to collision is T Ball 30 Smooth Horizontal

22 Three rods of identical cross sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B The points A and B are maintained at temperatures 7 and 2 T respectively In the steady state the temperature of the point C is T Assuming that only heat conduction takes place T T is 1995 2M b a 1 2 2 1 1 3 2 1 c 3 2 1 1 d 2 1

The potential energy of a particle of mass kg free to move along x axis is given by U x X 2 xj joule If total mechanical 2 energy of particle is 2J The maximum speed of particle will be 1 2m s 2 2 m s 3 5m s 4 5 m s der Course Rhac

A bicyclist comes to a skidding stop in 10 m During this process the force on the bicycle due to road is 200 N and is directly opposed to motion The work done by cycle on the road is 2000 J Zero 2000 J 20000 J

Illustrative Examples Ex 1 A uniform chain is hung up from two points at the same level and distant 2a apart If z is the sag at the middle show that z c cosh a c 1 If z be small compared with a show that 2cz a nearly

A free uniform disc of mass m 1 kg and radius R 1 m is rotating on smooth horizontal floor with angular velocity 10 rad s A particle of mass 2 kg is released from height 5 m above disc Particle hits disc at distance R 2 from centre of disc Collision of particle with disc is inelastic and particle sticks to disc after collision due to friction Disc does not bounce from ground during collision of particle with disc 21 22 23 w 10 Top view The friction force acting on particle after impact is A 25 4 N C 50 N The angular velocity of disc immediately after collision is A 5 rads B 10 rad s C 7 5 rad s D 12 5 rad s B 75 4 N D 50 3 N Wo M 1 kg The impulse on particle due to disc during impact is approximately A 20 2 Ns B 10 1 Ns C 10 Ns D 15 Ns side view 2 m h s R 2 and bet ho the Ca CC S C

Que 20 In a collinear collision a particle with an initial speed v strikes a stationary particle of the same mass If the final total kinetic energy is 50 greater than the original kinetic energy the magnitude of the relative velocity between the two particles after collision is v 2 O v 2 OV 4 Ovv2

147 A block slides down a curved track which is the quadrant of a circle of radius 5 m What will be the speed of the block at its bottom Assume that the surface is frictionless and g 10ms a 50 m s 1 c 5ms 1 b 10 ms d 1 ms 1

Energy of wave 8 A steel wire has a mass of 5g m and is under tension 450 N Find the maximum average power that can be carried by the transverse wave in the wire if the amplitude is not to exceed 20 of the wavelength Sol max Poug Porg max Vw A 2 2 2 MV W A 2 max Amax 201 a 2 Pavy 1 2 v 2 2

A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed A loop of 6 28 cm long thread is gently put on the film and the film is pricked by needle inside the loop The thread loop takes the shape of a circle Tension in the thread is surface tension of soap solution 0 03N m T cos 72 Option A B C D 62 T sin 7 8 8 2 1 5 x 10 4 N 3 x 10 4 N 2 x 10 4 N 4x10 4 N dl sin 62 T cos 732 Rate this questio

Calculate the angular frequency of the system shown in figure Friction is absent everywhere and the threads spring and pulleys are massless Given that mA mg m wwwwww 0 2k Ak O B

Motion under gravity 36 A body is projected vertically upward with speed 40 m s The distance travelled by body in the last second of upward journey is take g 9 8 m s and neglect effect of air resistance 1 4 9 m 4 19 6 m 2 9 8 m 3 12 4 m

A sustained three phase fault occurs in the power system shown in the figure The current and voltage phasors during the fault on a common reference after the natural transients have died down are also shown Where is the fault located V1 P V2 Transmission Line S V2 Transmission Line restbook T

Two particles A and B each of mass m are attached by a light inextensible string of length 21 The whole system lies on a smooth horizontal table with B initially at a distance I from A The particle at end B is projected across the table with speed u perpendicular to AB Velocity of ball A just after the string is taut is ku where k is A IS B

A bar with a mass of 8 kg is suspended from two springs such that when it is in equilibrium the springs make an angle of 45 with the horizontal as shown in the figure below Each spring has a stiffness of k 40 N m If the bar is pulled down by a small distance and released the natural perio of vibration will be 45 45 mon

5 A particle of mass 200 gm is moving in a circular path of radius 10 cm such that its tangential acceleration varies with time as at 6t m s What is the average power delivered to the particle by force acting on it in the first 10 sec The particle starts from rest

Consider a particle of mass m moving in one dimension under a force with the potential U x k x 4xl where the constant k 0 Show that the point x 21 corresponds to a stable equilibrium position of the particle Find the frequency of a small amplitude oscillation of the particle about the equilibrium position

5 A lead bullet of initial temperature 27 C and speed v kmh penetrates into a solid object and melts If 50 of the kinetic energy is used to heat it the value of v in km h is for lead melting point 600 K latent heat of fusion 2 5 x 104 Jkg specific heat 125 Jkg K a 3600 b 1800 c 1200 d 1000

7 How much work is done to build a column 4 8768 m high with 4 marble blocks each height 1 2192 m and mass 90 72 kg 1 A body of mass 10 kg is hung by two strings One of the strings is inclined at an angle of 60 with the vertical line What will be the angle of inclination of the other string with the vertical line so that the tension in that string will be minimum What are the tensions in the strings 2 Show that The principle of Multiplication of Thrust does not violet the conservation law of energy 3 Why a car gets bogged cannot proceed 4 why fluid pocess pressure energy although olid do not

71 A comet orbits the sun in a highly elliptical orbit Which of the following quantities remains constant throughout its orbit i Linear speed iii Angular momentum ii Angular speed iv Kinetic energy v Potential energy vi a i ii iii c iii and vi Total energy b iii iv v d ii iii and vi

a B The potential energy due to two particles separated by distance r is U 71 where 2 r a and are constants Find the distance between the two particles when they form a stable compound a b c d 7B 2 8p 7B 2 8p 1

A slider can slide on a smooth vertical elliptical guide as shown in the figure The fixed point O is located at one focus of the elliptical guide One end of spring is connected at O and the other end is connected to the slider The spring is unstretched when the slider is at A The speed vo given to the slider at A is such that the speed approaches to zero at C The semi major and semi minor axes are a and b respectively The acceleration due to gravity is g Determine the speed of the slider at B B

GM 100 10ms in free space Due to application 5 A solid sphere of mass M of radius R is moving with speed VR of external impulsive force it breaks into eight spheres of equal radius in such a way that the total mechanical energy before breaking and after breaking of a sphere remains same The speed of each sphere in m s when separation between them is very large is found to be 100x Find the value of x assume at that instant speed of each sphere is same arhit around the earth with a speed equal to half the magnitude escape

A raindrop falling from a height h above the ground attains the terminal velocity when it has 4 fallen through a heighth The diagrams shown 5 in figure which correctly shows the change in potential and kinetic energy of the drop during its fall up to ground is 1 3 h 55 h h 6 5 5 KE PE PE KE 2 t t h SI5 4 h 6 5 PE XKE t PE KE t

0 A zener diode having breakdown voltage equal to 15V is used in a voltage regulator circuit shown in figure The current through the diode is 2011M oWW 250Q 20V a 10mA c 20 mA 15V ww b 15mA d 5 mA 1kQ2