Work, power & energy Questions and Answers

of a two particle system depends only on the separation between the two particles The most appropriate choice for the blank space in the above sentence is a Kinetic energy c Potential energy b Total mechanical energy d Total energy

D A particle is rotated in a vertical circle by connecting it to a string of length 1 and keeping the other end of the string fixed The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is a gl b 2gl c 3gl d 5gl

16 Find the reading of the spring balance shown in figure 5 E6 The elevator is going up with an acceleration of g 10 the pulley and the string are light and the pulley is smooth 17 A block of 2 kg is suspended f A 9 10 A 3kg B 1 5kg

54 A satellite in force free space sweeps stationary interplanetary dust at a rate of dM dt av where M is mass and v is the speed of satellite and a is a constant The acceleration of satellite is ap a c 2M 2av M b av av M 1994

24 A system of particles is free from any external force If and a be the velocity and acceleration of the centre of v mass then it necessarily follows that a 0 a 0 c v 0 0 b v 0 a 0 d None of these 31

3 Two equal masses are attached to the two ends of a spring of spring constant k The masses are pulled out symmetrically to stretch the spring by a length x over its natural length The work done by the spring on each mass is a 12 kx b kx c 2 2 2 kx d kx 4 2

2 A ball is rolling along a level frictionless surface with a speed v 25 m s when it encounters a ramp that is inclin at 8 28 How far does it roll along the surface of the ramp d before coming to a rest Make sure to include a fully labeled free diagram with each and please show your reasoning steps calculations I e d

D A solid iron sphere A rolls down an inclined plane while the plane in a frictionless manner At the bottom of the an identical hollow sphere B of same mass slides down inclined plane the total kinetic energy of sphere A is a less than that of B b equal to that of B c more than that of B a more and sometimes less

4 Stretching a Spring If a force of 80 N is required to hold a spring 0 3 m beyond its unstressed length how much work does it take to stretch the spring this far How much work does it take to stretch the spring an additional meter

88 A force of 14 N acts on a particle along the ve 31 2 6k If the particle displaces from 0 0 0 to 2 4 2 the work done W F S by force or the particle is 1 10 J 2 52 1 2 19

A collar B of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m The spring lying in the plane of the circular track and having spring constant 200 Nm is undeformed when the collar is at A If the collar starts from rest at B the normal reaction exerted by the track on the collar when it passes through A is

work is done against gravity W m g h 10 x 9 Es x is pulled across a floor by applying a force of 10 0 degrees above the horizontal How much work ying force in pulling the object to a distance of 8m sider the following figure N 100 sin 60 A 60 100 N 100 sos 60 Tw orce of 100 N is applied to a box of weight W Force is plied at angle 60 It has two components horizontal 5 60 and vertical component 100 sin 60 The horizon e force should be considered here because it causes the rizontal W 100 cos 60 x 8 100 x 0 5 x 8 400 J

A farmer hitches her tractor to a sled loaded with firewood and pulls it a distance of 20 m along level ground Fig 6 7a The total weight of sled and load is 14 700 N The tractor exerts a constant 5000 N force at an angle of 36 9 above the horizontal as shown in Fig 6 7b There is a 3500 N friction force opposing the sled s motion Find the work done by each force acting on the sled and the total work done by all the forces

the volume of the car Two objects are moving at a speed of 8m sec and 12 m sec respectively If they are on the same surface then the ratio of their potential energy will be A 4 9 B 1 1 Uttrakhand NTSE Stage 1 2015 D None of the above C 2 3 A man of 80 kg mase

7 A solid sphere of mass M of radius R is moving with speed GM 100 10ms 1 in free space Due to R application 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

A block of mass 1 0 kg placed on a horizontal floor is attached to a fixed mail with the help of a spring of stiffness 5 0 N cm Coefficient of friction between the block and the floor is 0 25 The block is pulled away from the nail stretching the spring by an amount 8 5 cm and released Find the final deformation of the spring when the block stops How many times did the spring become relaxed during this process Acceleration of gravity is 10 m s

7 In the setup shown an almost inertia less bar is suspended horizontally with the help of two identical springs each of stiffness k two light inextensible cords that pass over fixed ideal pulleys and two counterweights each of mass m A small disc of mass 0 01m is placed at the midpoint of the bar A block of mass 1 99m is suspended from the disc with the help of a light cord that passes through a hole in the bar If this cord is cut up to what maximum height will the disc jump m eremerevereree 0 01m Ce www memme 1 99m

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle from the vertical see figure The normal reaction of the track on the particle vanishes at point Y where OY makes angle with the horizontal Then 1 sin cos 0 3 sin 3 sin 2 3 cose 1 2 sin cose 2 3 4 4 sin cose mg Y 2014

Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R If they attract each other due to gravitational force only then the distance covered by the smaller body just before collision is 1 2 5R 2003 3 7 5R 2 4 5R 4 1 5R two statements 2003

The Work Energy theorem A does not hold in all inertial frames Bis independent of Newton s second law C may be viewed as a scalar form of Newton s second lav D cannot be extended to non inertial frames E is independent of Newton s third law Space for rough work

A centigrade and a Fahrenheit thermometer are dipped in boiling water Now the water temperature is lowered untill Fahrenheit thermometer registers 140 The fall in temperature registered by centigrade thermometer is 1 40 C 3 72 C 2 30 C 4 60 C 140 32 188 2 108 18

A particle of mass 2 kg executes SHM under a force F 50x where x is in m and F in N If it crosses the mean position x 0 with a speed 10 m s its mechanical energy is 75 J Find potential energy of particle when it is at x 1 m 1 O J 2 25 J 3 25 J 4 100 J

A wind powered generator converts wind energy into electrical energy Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electric energy For wind speed v the electrical power output will be most likely proportional to 1 v 3 v 2 v 4 v 2013 horizontal plane with a

A particle of mass 2 kg is attached with a spring of stiffness 72 N m When block is at x 1m it moves with maximum speed The block moves with 24 m s while passing through x 4m Find out the x coordinates in m where it s velocity will be zero 2 5 6 4 None of these 1 4 6 3 4 1 9

Example 11 2 A porter lifts a luggage of 15 kg from the ground and puts it on his head 1 5 m above the ground Calculate the work done by him on the luggage

A spring of spring constant 5 x 10 N m is stretched initially by 5 cm from the unstretched position Then the work required to stretch is further by another 5 cm is 1 12 50 N m w 1XK 2 2003 3 25 00 N m W 25 X 10 2 18 75 N m 4 6 25 N m

If a bullet is fired from a gun then a the mechanical energy of bullet gun system remain constant b the mechanical non mechanical energy is converted into energy C the mechanical energy may be conserved d the non mechanical energy is converted into mechanical energy

A copper block of mass I kg slides down on a rough inclined plane of inclination 37 at a constant speed Find the increase in the temperature of the block as it slides down through 60cm assuming that the loss in mechanical energy goes into the copper block as thermal energy Specific heat of copper 420 J kg K g 10ms2 88 1 6 6 x 10 3 C 2 7 6 x 10 3 C 3 8 6 x 10 3 C 4 9 6 x 10 3 C

3 30J The work done at the end of displacement 20cm according to the F 1 1 J 10 N 5 10 10 mJ 20 50 60 70 3 3 J 1 4 40J x graph is x m 4 43 y direction The Kinetic energy

10 A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s It collides with a horizontal spring of force constant 200 N m The maximum compression produced in the spring will be 1 0 7 m 2 0 2 m 3 0 5 m 4 0 6 m AIPMT Mains 2012

With what velocity should a student of mass 80 kg run so that his kinetic energy becomes 320 J

Xo Calculate the net work done by the force F whose variation with position has been shown as above T 1 FOX 4 2 X RIN Yo

0 An engine pumps water continuously through a hole Speed with which water passes through the hole nozzle is v and k is the mass per unit length of the water jet as it leaves the nozzle Find the rate at which kinetic is being imparted to the water energy 112 kv a kv b 2 c 12 2k d 1 3 2k

In the arrangement of resistances shown in the Fig 9 9 the pd between B and D will be zero when the unknown resistance X is a 4 S c 32 120 452 www 4 92 B wwww 12 D b 0 5 d 12 22 252 wwww C

a A particle of mass m slides on a frictionless surface ABCD starting from rest as shown in Fig 8 248 The part BCD is a circular arc If it looses contact at point P the maximum height attained by the particle from point C is A 2R R2 C 3R E 1 2 2 B Fig 8 248 R C P 45 R D b R1 R 2 2 in d None of these

d None 75 A mass m starting from A reaches B of a frictionless track On reaching B it pushes the track with a force equal tox times its weight then the applicable relation is x 5 2 a h c h r h r A Fig 8 253 B b h r 2 d h x 1 2 r

In the arrangement shown the pulley and the strings are ideal The acceleration of block B is A g5 C 2g 5 B g2 D 2g 3 m mB

A block of mass 10 kg is released on a fixed wedge inside a cart which is moved with constant velocity 10 m s towards right Take initial velocity of block with respect to cart zero Then work done by normal reaction on block in two second m ground frame will be g 10 m s A zero B 960 J 10kg 37 10 m s C 1200 J D none of these OR and path 2

A block C of mass m is moving with velocity vo and collides elastically with block A of mass m and connected to another block B of mass 2m through a spring of spring constant K Find the value of K if Xo is the compression of the spring when velocities of A and B are same 1 mv 2 Xo 3 mv2 Vo A www 2 B smooth m 2x 2 2 mv2

O 9 A thin uniform rod pivoted at O is rotating in the horizontal plane with constant angular speed as shown in the figure At time t 0 a small insect starts from O and moves with constant speed v with respect to the rod towards the other end It reaches the end of the rod at t T and stops The angular speed of the system remains throughout The magnitude of the torque 7 about O as a function of time is best represented by which plot A C 7 171 T T t B D 171 O T 33 2012 t t

The diagram shows a force extension graph for a rubber band Consider the following statements Extension Force I It will be easier to compress this rubber than expand it II Rubber does not return to its original length after it is stretched II The rubber band will get heated if it is stretched and released Which of these can be deduced from the graph 2 II and III 4 I only 1 III only 3 I and III 0

0 A mass of 0 5 kg moving with a speed of 1 5 m s on horizontal smooth surface collides with a nearl weightless spring of force constant k 50 N m Th maximum compression of the spring would be a 0 15 m c 1 5 m b 0 12 m d 0 5 m a

A simple pendulum of length L having a bob of mass m is deflected from its rest position by an angle and released figure 8 E16 The string hits a peg which is fixed at a distance x below the point of suspension and the bob starts going in a circle centred at the peg a Assuming that initially the bob has a height less than the peg show that the maximum height reached by the bob equals its initial height b If the pendulum is released with 0 90 and x L 2 find the maximum height reached by the bob above its lowest position before the string becomes slack c Find the minimum value of x L for which the bob goes in a complete circle about the peg when the pendulum is released from 0 90 0 IX

89 A bead of mass 1 2 kg starts from rest from A to move in a vertical plane along a smooth fixed quarter ring of radius 5 m under the action of a constant horizontal force F 5 N as shown in Fig 8 263 The speed of bead as it reaches point B is B F R 5 m Fig 8 263 a 14 14 ms b 7 07 ms 1 A c 5 ms d 25 ms

A bullet looses th of its velocity passing through one plank The number of such planks that 2014 are required to stop the bullet can be n 1 2n 1 3 infinite 2n n 1 2 4 n Statemer

18 9 The potential energy of a 1 kg particle free to move along the x axis is given by 2 U x 4 X 4 X 2 The total mechanical energy of the particle 2 J Then the maximum speed in m s is 1 2 3 2 2 3 2 4 1 2

3 A bob is suspended from a crane by a cable of length 1 5 m The crane and load are moving at a constant speed vo Fig 5 15 The crane is stopped by a bumper and the bob on the cable swings out at an angle of 60 The initial speed vo is g 9 8 m s 20

A particle is moving along x axis under the action of a force F which varies with its positio 1 x as Fx Find the variation of power due to this force with x VX Hint F x x 2 a or vdv dx Po 1 2 vdv k x dx Find v P Fv kx 1 2 V x a kx 1 2

5 Calculate the angle 0 for which if the particle A is released it undergoes perfectly elastic collision with another identical mass B placed at rest and B is found to just reach the horizontal position of its string 1 30 3 37 2l LL B l 2 60 4 53

A body falling from a vertical height of 10 m pierces through a distance of 1 m in sand It faces an average retardation in sand equal to g acceleration due to gravity 1 g 2 9g 3 100g 10 m 11 m