Newton's law of motion Questions and Answers

08 Laws of Motion 7 Tension in the blocked the distance x from right end F L X L Tx H Force is applied at both right and left end The acceleration of the system is given by F a M M M3 F F 1x M 8 T 5x F L X 9 Let F and F be the contact forces between M M and M M3 respectively smooth M TTTT smooth F

When a cannon shell explodes in mid air then momentum of the system is conserved because 1 Gravity doesn t affect the momentum of the system 2 Gravity is not acting during collision 3 impulsive force is very large compared to the gravity 4 Gravity is very large compared to impulsive force

Two balls of charges q and q2 initially have exactly same velocity Both the balls are subjected to same uniform electric field for same time As a result the velocity of the first ball is reduced to half of its initial value and its direction changes by 60 The direction of the velocity of second ball is found to change by 90 The electric field and initial velocity of the charged particle are inclined at angle 1 60 3 90 2 30 4 150

A balloon of mass M is descending with a constant acceleration g 3 When a mass m is released from the balloon it starts rising with the same acceleration g 3 The value of m is Assuming that its volume does not change 1 M 2 2 M 4 3 4M 4 2M

The figure shows an L shaped body of mass M is placed on smooth horizontal surface The block A is connected to the body by means of an inextensible string which is passing over a smooth pulley of negligible mass Another block B of mass m is placed against a vertical wall of the body Find the minimum value of the acceleration of block A so that block B remains stationary relative to the wall Coefficient of friction between the block B and the vertical wall is u 2 Take g 10 m s m B a gr 7

6 A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position The knives are at a distance d from each other The centre of mass of the rod is at distance x from A The normal reaction on A is 1 3 W d x d Wd 2 4 WX d AIPMT 2015 W d x

22 A body of mass 1 kg initially at rest explodes and breaks into three fragments of masses in the ratio 1 1 3 The two pieces of equal mass fly off perpendicular to each other with a speed of 30 m s each What is the velocity of the heavier fragment a 10 m s b 20 m s c 10 2 m s d 30 2 m s

2 Two uniform solid cylinders A and B each of mass 1 kg are connected by a spring of constant 200 Nm at their axles and are placed on a fixed wedge as shown in the Fig 6 325 There is no friction between cylinders and wedge The angle made by the line AB with the horizontal in equilibrium is a 0 A doo 0 0 0 B 60 Fig 6 325 30 b 15

5 A police van moving on a highway with a speed of 36 km h fires a bullet at a thief s car speeding away in the same direction with a speed of 108 km h If the muzzle speed of the bullet is 140 ms with what speed will the bullet hit the thief s car a 120 ms c 140 ms b 130 ms d 150 ms

3 In the arrangement shown in Fig 6 335 if the acceleration of B is a then find the acceleration of A a a sin a b a cot e Fig 6 335 c a tan 0 d a sin a cot 0 cos Fixed incline

11 0 Two blocks are in contact on a frictionless table one has a mass m and the other 2 m as shown in figure Force F is applied on mass 2m then system moves towards right Now the same force F is applied on m The ratio of force of contact between the two blocks will be in the two cases respectively a 1 1 b 1 2 c 1 3 d 1 4 2m m F

A A force F 15 kg is placed over a frictionless horizontal surface Another block of mass 10 kg placed over it that is connected with a light string passing over two pulleys fastened to the 15 kg bloc 80 N is applied horizontally to the free end of the string Friction coefficient between tv blocks is 0 6 The portion of the string between 10 kg block and the upper pulley is horizontal as show in figure Pulley string connecting rods are massless Take g 10 m s 10 kg P 0 6 15 kg Smooth The magnitude of acceleration of the 10 kg block is A 3 2 m s B 2 0 m s C 1 6 m s F 80 N D 0 8 m s If applied force F 120 N then magnitude of acceleration of 15 kg block will be A 8 m s B 4 m s C 3 2 m s D 4 8 m s

A particle slides down from the top outside smooth surface of a fixed sphere of radius a 10 m The initial horizontal velocity to be imparted to the particle at the top is 5K m s if it leaves the surface at a point whose vertical height above the centre of sphere is 3a 4 Find the value of K

m Three blocks A B and C are suspended as shown in the figure Mass of each block A and C is m If system is in equilibrium and mass of B is M then A M 2m B M 2m C M 2m D M m Corp Reg Office CG Tower A 46 52 IPIA Near City Mall Jhalawar Road Kota Raj 324005 in E mail contact resonance ac in ADVNI 49 B

1 In the a lite guard is stationed at A on a beach and a child is swimming at B in the river The life guard can run at a speed of 2 m s and can swim with a speed of 1 m s He observes that the child is drowning and rushes to save the child If he runs in the direction shown by the angle e so that he reaches B in the shortest possible time to save the child then A 1 1 M 0 PN COSO COS B 2 2 4 4

The three flat blocks in the figure are positioned on the 37 incline and a force parallel to the inclined plane is applied to the middle block The upper block is prevented from moving by a wire which attaches it to the fixed support The masses of three blocks in kg and coefficient of static friction for each of the three pairs of contact 0 3 surfaces is shown in the figure Determine the maximum value which force P may have before slipping take P 0 4 30 50 37 40 0 5

5 Two rails of a railway track insulated from each other on the ground are connected to a millivoltmeter The reading of millivoltmeter when train travels at a speed of 20 m s along the track is Given B 0 2 x 10 4 Wb m and distance between the rails is 1 m D F S 1 10 mV 3 40 mV 2 0 4 mV 4 4 m 8

lections on concepts What is a force What changes can be produced by a Force AS Give two examples each for a contact force and a force at a distance 6 Tension force direction is called a Muscular force

4 points Zach whose mass is 75 kg is in an elevator that is ascending at 10 m s The elevator takes 5 0 s to brake to a stop at the tenth floor a Zach s apparent weight before the elevator starts braking is A 585 N B 885 N b Zach s apparent weight while the elevator is braking is A 585 N B 885 N C 735 N C 735 N D 450 N D 450 N

7 A block of mass m is placed in contact with one end of a smooth tube of mass M A horizontal force F acts on the tube in each case i and ii Then F b am am c amaM m m a a 0 and am F M m Fig 6 362 Force on mis F M m F M in i in i in ii mF in ii M M 1 ii

Calculate i asystem ii FDE ii FCD iv FBC v FAB Corrosponding to the following diagram A B D E P m m C m m m

and iv 10 An isolated charge q1 of mass m is suspended freely by a thread of length 1 Another charge q2 is brought near it r 1 When q is in equilibrium tension in thread will be a mg b mg c mg d none of these Thro 92 r 1 91 4 Three identica radius R are k other two The sphere due to t a c 1 9 ATE R 3 16TE F

A block of mass m is attached to a uniform string of mass 3m and lenght L as shown in the figure The lift is moving upward with accleration a g 3 The tension in the string at point P is P 3 3 4

A ball is projected vertically upwards crosses a point at a height h after time 3 s and 5 s Initial speed of throw of the ball is g 10 m s 1 20 m s 40 m s A 3 10 m s 4 60 m s

44 The magnitude of relative acceleration of A w r t B is Assuming pulley and string are light and massless 7777 1 F4 3 2F m 4F 3m A m O Smooth 2m 2 B 4 TTTTT Horizontal floor 3F 2m F

40 A block of mass 10 kg is placed on a rough horizontal surface of coefficient of friction 0 5 The minimum force required to move the block is g 10 m s 1 20 3 N 3 50 N 2 50 3 N 4 20 5 N

In the arrangement shown in Fig 5 62 show that the tension in the string between masses and m M3 2m m3 8 is T

3 4 A block of mass m is kept in an elevator which starts moving downward acceleration a as shown in figure The block is observed by two observers A and B for a time interval to The observer B finds that the work done by gravity is 1 A mg t B mg t The observer B finds that work done by normal reaction Nis B Nat 2 A zero C 5 According to observer B the net work done on the block is 1 Bma t A ma t mgat C Nat 2 1 2 mgat 2 D mg D None D

6 Consider the system of two blocks shown in the figure 4 kg 6 N 8 N 9 kg 45 N 70 N A What is the net force acting on the entire two block system B Find the acceleration of the system C What force is exerted on the 4 kg block by the connecting string and what is the direction of this force D What force is exerted on the 9 kg block by the connecting string and what is the direction of this force

For what minimum value of m the block of mass m 20 kg will leave the contact with surface mom m

A Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of 1 Statement B Both Statement 1 and Statement 2 are true but Statement 2 is not the correct explanation of Statement 1 C Statement 1 is true Statement 2 is false D Statement 1 is false Statement 2 is true Statement 1 A body is lying at rest on a rough horizontal A person accelerating with acceleration ai where a is positive constant and i is a unit vector in horizontal direction observes the body with respect to him The block experiences kinetic friction as observed by the person Statement 2 Whenever there is relative motion between the contact surfaces then kinetic friction acts

D Tension in string is 3mg 5 In the arrangement shown in figure pulleys and strings are ideal End A of string connected to pulley P is moved upwards with acceleration aA 2 m s while end B of another string shown in figure is moved up with acceleration ag 1 m s2 Block C of mass 1 kg is moving up with acceleration 1 m s If block D to which strings are connected symmetrically moves such that its orientations remains same then assume g 10 m s A acceleration of block D is m s upwards B end A is pulled with force of 22 N C mass of block B is kg D acceleration of block B is 7 3 m s upwards ag 1 m s B T ac 1 m s aA 2 m s A47 P 27 21 B AT 1 kg Im i D TAK

45 D 1 2 m s Two masses A and B are connected with two an inextensible string to write constraint relation between v V Student A VA cos 0 VB Student B V COS 0 VA A A is correct B is wrong C both are correct B www OVB VA B B is correct A is wrong D both are wrong Find velocity of ring B v at the instant shown The string is tout and

27 In figure 5 E11 m 5 kg m 2 kg and F 1 N Find the acceleration of either block Describe the motion of m if the string breaks but F continues to act m G FY m2 YF

3 Explain Gravitational Force by giving a suitable example AS 4 Draw and explain a free body diagram FBD to show all the forces acting on a car AS 5 Why do tools meant for cutting always have sharp edges AS Application of concepts 1 How can you differentiate between a contact force and a force at a distance AS 2 Find the net forces from the following diagrams 8N abo 12N b 8N 8N 8N CON d 9N

length 1 80 cm and mass m 2 kg is hanging from the end of a plane so that the length 1 of the vertical segment is 50 cm as shown in the figure Th other end of the chain is fixed by a nail At a certai instant the nail is pushed out what is the velocity of th chain at the moment it completely slides off the plan

A body of mass 5 kg under the action of constant force F F1 F has velocity at t 0s as U 61 21 m s and at t 10s as 6j m s The force F is JEE Mains Online 2014 3 4 a 31 41 N b 1 N c N d 3 4 N 5

26 Calculate the tension in the string connected between the 1 kg and 3 kg masses o 4 kg 1 30 N 3 50 N 3 kg 1 kg f 2 40 N 4 60 N 4 kg

3 A block of mass 10 kg is held at rest against a rough vertical wall 0 5 under the action a force F as shown in figure The minimum value of F required for it is g 10 m s 10 kg 30

A weight of 150 kg is hanged at distance of 60 54 cm from one end of 1 5 m long pole If both the ends of pole are rested on the shoulder of two person then the weight lifted by both the persons are A 30 and 120 kg C 100 and 50 kg B 60 and 90 kg D 75 kg each

Two blocks A and B are held in position by a rod AB as shown in figure below The weight of block B is 1000N Find the weight of block A such that block will not slide away from wall Take angle of friction for all contact surfaces as 15 20 Two Blocks A and I are held in position by The weight of block B is 1000N Find the weight slide away from wall Take angle of fricion for a Problem nad AB as shown in lock A such that the 15

Three spring balances are attached to the ring as shown in the figure There is an angle of 90 between the balance A and balance B There is a reading of 5 N on balance A and 12 N on the balance B and reading in the balance C is 13 N and angle 0 is 33 7 x Find the value of x 000000 C TURNO 90 000000 A

D None of these the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure 2m s www 1m s A 3 2 m s B 3 2 m s C 1 2 m s D 1 2 m s Two masses A and B are connected with two an inextensible string to write contr

A small ball of density 4p is left from the surface of liquid The density of liquid varies as p p 1 ay where y is height of liquid from the surface and po a are constants The time 2 period of oscillation of ball is found to be sec Find K a 2 m g 10 ms2 Neglect K viscosity

Q1 Action and reaction forces act a on different bodies always c on same body sometimes b on same body always d On different bodies sometimes

O mass m rests on the plank B of mass 3m which is free a 0 c to slide on a frictionless horizontal surface The coefficient of friction between the block and plank is 0 2 If a horizontal force of magnitude 2mg is applied to the plank B the acceleration of A relative to the plank and relative to the ground respectively are bol c g 2 B 3g g 5 5 b 0 A d 2g 3 00 10 2g g ool 2mg 5 5

6 Four blocks of same mass m connected by cords are pulled by a force F on a smooth horizontal surface Determine the tension T 72 and T3 F M M To M T M

1kg 1kg Smooth surface T T 3 3kg In following diagram find value of T 2 1 12 N 2 6 N 3 4 N 4 1 N

A box of dimension H x B x R is kept on a frictionless inclined plane as shown in the figure A stone is thrown from one corner P with speed u parallel to the ceiling of the box such that it hits the floor of the box at the opposite body diagonal point Q At the same instant the box is released to slide down the plane Calculate the time of flight B

2 3 4 Two small rings O and O are put on two vertical stationary rods AB and A B respectively One end of an inextensible thread is tied at point A The thread passes through ring O and its other end is tied to ring O Assuming that ring O moves downwards at a constant velocity v then velocity V2 of the ring O when ZAOO a is a V C V 0 B 2 sin 2 cos a 3 cos 2 a Fig 6 327 450 B VI b V 2 cos a 2 sin a d None of these 5 28