Newton's law of motion Questions and Answers

A uniform rope of length lies on coefficient of friction is u then the maximum len x of the part of this rope which can overhang fro the edge of the table without sliding down is 1 1 l 2 l U 1 e

14 A cricket ball of mass 150 g moving with a speed of 126 kmh hits at the middle of the bat held firm at its position by the batsman The ball moves straight back to the bowler after hitting the bat Assuming that collision between ball and bat is completely elastic and the two remain in contact fo 0 0015 the force that the batsman had to apply to hold the bat firmly at its place would be NCERT Exemp a 10 5 N 11 05 104 N b 21 N d 2 1 104 N

2 A horizontal uniform plank is supported by ropes I and II at points P and Q respectively as shown above The two ropes have negligible mass The tension in rope I is 150 N The point at which rope II is attached to the plank is now moved to point R halfway between point Q and point C the center of the plank The plank remains horizontal Which of the following are most nearly the new tensions in the two ropes Tension in I A B C D 75 N 100 N 112 5 N 112 5 N 150 N Tension in II 225 N 200 N 112 5 N 187 5 N 300 N

W A box of dimensions 1 and b is kept on a truck moving with an acceleration a If box does not slide maximum acceleration for it to remain in equilibrium with respect to truck is b a c g a b gb 1 d None of these

A bat hits a 0 150 kg baseball for 0 0880 s The ball s velocity changes from 41 0 m s left to 37 0 m s right How much force was applied to the ball Unit N Remember right is left is Enter

Three blocks A B and C of masses m m 2 and m respectively are of different densities and dimensions as shown in the figure The coefficient of frictions are shown Blocks placed in a vertical line are made to move towards right with same velocity at the same instant Find the time in sec taken by the upper block A to topple from the middle block B Assume that blocks B and C don t stop sliding before A topples from B given L 36m 0 4 and g 10m s A W 4 L 4 B W 2

0 The breaking strength of the string connecting wall and block B is 175N find the magnitude a weight of block A for which the system will be stationary The block B weights 700 N g 10 m s B vitoagen 30

A block of mass placed on a rough 30 can inclined plane of inclination be just prevented from sliding down by applying a force F up the plane and it can be made to just slide up the plane by applying a force F up the plane If the coefficient of friction between the block and the inclined plane is 3 then F2 F is

A horizontal force F produces an acceleration of 6 m s2 on a block resting on a smooth horizontal surface The same force produces an acceleration of 3 m s on a second block resting on a smooth horizontal surface If the two blocks are tied together and the same force acts the acceleration produced will be

A solid cylinder of radius 10 cm and length 1 m clamped from its one end is twisted through an angle of 0 4 rad by applying torque at another free end The shear strain developed in the cylinder will be 1 0 2 2 0 8 3 0 02 4 0 04

A metre stick of mass 400 g is pivoted at one end and displaced through an angle 60 The increase in its potential energy is O2J O 3J 00 16 0 1

A 120 kg box is initially at rest when a student pushes it with 450 N of force for 1 5 s There is negligit friction between the box and floor What is the best estimate of the speed of the box after the 1 5 s time interval Assume rightwards is the positive direction Choose 1 answer Choose 1 answer 7 2 4 9 m S m

A block takes twice as much time to slide down a rough 45 inclined plane as it takes to slide down an identical smooth 45 inclined plane The coefficient of kinetic friction between the block and rough inclined plane is

e 0 5 g 10 m s A ball is thrown vertically upward from ground with speed 40 m s It collides with ground after returning the total distance travelled and time taken during its bouncing e 0 5 g 10 m s SC ng and rebounds If e 0 2 is the coeffici 11 C

A hanging block of mass m prevents the smaller block of mass m from slipping over a movable triangular block of mass M All the surfaces are frictionless and the strings and the pulleys are light Value of mass m in terms of m M and is TTTT m M TIIT 0 TIT m

9 In a smooth horizontal groove two particles m and m collide first collision takes place at t 0 Radius of the circular grove is R 1 2 3 4 m m Column I If m m and both are moving in opposite direction with speed v then time of 2nd collision e 1 If m is at rest and m 2m and e 1 then time of 2nd collision mi collides with velocity v A 1 p 2 q 3 r 4 t C 1 r 2 q 3 p 4 q If m is at rest m collides with velocity v m m and e 1 then time of 3rd collision p 9 If m is at rest m collides with velocity v m m and e r then time of 2nd collision e Column II 2 R S t B 1 q 2 p 3 r 4 r D 1 q 2 p 3 t 4 r V TR V 4TR V 3TR V TR 2V

In the following figure the masses of the blocks A and B are same and each equal to m The tensions in the strings OA and AB are T and T respectively The system is in equilibrium with a constant horizontal force mg on B The tension T is 1 ma 2 2mg m A m B 3 mg 3 mg 4 5mg

Q4 In the given circuit a charge of 80 C is given to the upper plate of the 4 F capacitor Then in the steady state the charge on the upper plate of the 3 F capacitor is 80 C 2 mF 4 mF a 32 C b 40 C c 48 C d 80 C 3 mF 2

A point object moves on a circular path such that distance covered by it is given by function S 2t meter t in 2 second The ratio of the magnitude of acceleration at t 2s and t 5 s is 1 2 then the radius of the circle is A 1m B 3 51 m

Two blocks are connected by a string as shown in the diagram The upper block is hung by another string A force Fapplied on the upper string produces an acceleration of 2m s in the upward direction in both the blocks If Tand T be the tensions in the two parts Takeg 10m s 2 kg

More than one 13 A point object of mass m is slipping down on a smooth hemispherical body of mass M and radius R The poin object is tied to a wall with an ideal string as shown At a certain instant speed of the hemisphere is vand acceleration is a Then speed v and acceleration a of a particle has value Assume all the surfaces in conta are frictionless A v v sin 60 C a a me 30 R B v v D a R 3 a 2

Rocket engines lift a rocket from the earth surface because hot gas with high velocity O Push against the earth Push against the air React against the rocket and push it up Heat up the air which lifts the rocket

Q 19 Force Fo Moderate O 4 1 Time A particle of mass m initially at rest is acted upon by a variable force F for a brief interval of time T It begins to move with a velocity u after the force stops acting F is shown in the graph as a function of time The curve is a semicircle 00 58 T O 000

A bomb of mass 10 kg explodes into two fragments of masses 4 kg and 6 kg The velocity of 4 kg is 10 m s Determine the loss of mechanical energy in the form of explosion A 333 3 J B 300 J c 250 J

A block of mass m 2kg of shown dimensions is placed on a plank of mass M 6Kg which is placed on smooth 1 If a horizontal force F is 3 horizontal plane The coefficient of friction between the block and the plank is u applied on the plank then find the maximum value of F in N for which the block and the plank move together I H 4 m M F

d 1 m s towards right 35 In the diagram shown in figure both pulleys and strings are massless The acceleration of 2 kg block is a 2 5 m s 1 c 7 5 m s 1 1 kg F 100N 2 kg 3 kg b 5m s 1 d 10 m s 1

Two particles of masses 10 kg and 35 kg are connected four strings at points B and D as shown in figure Determine the tensions in various segments of the string A 30 37 100 N C 350 N D

Q5 Find the magnitude of acceleration of block A and B just after the string is cut a g 2 g b g g c 8 2 8 2 B T mg d g 0 Step 1 Find All Forcesunder equilibrium A F T mg F 2mg mg 0000000 771 B m

Q5 A money is descending from the branch of a tree with constant acceleration If the breaking strength is 75 of the weight of the monkey the minimum acceleration with which monkey can slide down without breaking the branch is a g b c d 3g 9

47 A block of unknown mass is at rest on a rough horizontal surface A force F is applied to the block The graph in the figure shows the acceleration of the block with respect to the applied force The mass of the block is Acceleration ms a 1 0 kg c 20kg 7654321 2 4 6 8 10 12 14 Applied force F N b 0 5 kg d 15 ko

Find the min move on rough surface for any value of applied force F coefficient of static friction between the block and surface is A tan C cot A B d TO 1 A railway track is banked for a speed v by making the height of the out of the inner rail The horizontal separation between the rails is d The r track is r then which of the following relation is true h B tan sin tan u D cot 2 V rg

inclined 30 above the horizontal The coefficient of kinetic friction between the skier and the slope is 0 10 Which of the following best describes the acceleration of the skier A It is zero B It is about 4 0 m s C It is about 9 0 m s D It is about 10 m s E It cannot be determined without knowing th

A block is placed on an inclined plane and remains stationary as shown in the figure above A student claims The block remains stationary because as gravity tries to pull the block down the ramp the block exerts an equal and opposite force on itself up the ramp Is the student s claim correct Justify your answer A B C D Yes Newton s first law states the block must remain stationary unless pushed Yes Newton s third law states the block must exert a force equal and opposite to gravity No Newton s first law states the block s inertia must cause it to move down the ramp No Newton s third law states the block cannot exert a force on itself

5 When two bodies are connected by a light string passing over a light pulley for m T m g m a for m m g T m a Acceleration of each body m m m m 2m m g m m a T g T al MI T m2 m2 m1 a

Consider a mass pulley system as shown in the figure There is a wedge of mass M and equa wedge angles lying on a rigid horizontal table The coefficient of friction between the wedge and the table is There are two blocks of mass m and my lying on the incline of the wedge Th coefficients of friction between the blocks and wedge are and 2 as shown in the figure Conside m m and the coefficients of friction and to be less than tan Gravity is actin downwards with acceleration due to gravity g What should be the value of so that the syster is in equilibrium m m X 1 3 m X21 Cose sin 0 2 sin cos X4 12 cos sin 0 sin cos H cos 0 sin 0 sin cos cos sin 0 M

Two smooth rings A and B are connected by a string Another string connects ring A and a block moving do with velocity 12 m s If strings are tight then at given moment Vertical Horizontal O O UB VB 15 m s 24 m s y 12 m s

A cracker is thrown into air with a velocity of 10 m s at an angle of 45 with the vertical When it is at a height of 0 5 m from the ground it explodes into a number of pieces which follow different parabolic paths The velocity of centre of mass of the system after explosion when it is a height of 1 m from the ground g 10ms 2 is 1 4 5 ms 2 2 5 ms 3 5 4 m s 4 10 ms

In the setup shown a block is placed on a frictionless floor the cords and pulleys are ideal and each spring has stiffness k The block is pulled away from the wall How far will the block shift while the pulling force is increased gradually from zero to a value F b a 2F 5k SF 9k d 10F 3k 10F 9b

3 Choose the wrong statement 1 In the process of explosion some changes may occur in momentum of individual fragments due to internal forces but the motion of the centre of mass is unaltered 2 Motion of centre of mass depends upon the external force 3 The location of centre of mass depends on the reference frame used locate it 4 The position of centre of mass depends upon the shape of the body and the distribution of mass

A block of mass M is hanged by a light spring of force constant k to the top bar of a reverse U frame of mass M on the floor The block is pulled down from its equilibrium position by a distance and then released The minimum value of a such that the reverse U frame will leave the floor momentarily is M M g k oooooooo M M Correct Answer

min form metallic rod rotates about its perpendicular bisector with constant angular speed If it is heated uniformly to raise its 1 25 temperature slightly 1 Its speed of rotation increases 2 Its speed of rotation decreases 3 Its speed of rotation remains same 4 Its speed of rotation increases because its moment of inertia increases body of mass of

SO 0 An empty plastic box of mass m is found to accelerate up at the rate of g 6 when placed deep inside water How much sand should be put inside the box so that it may accelerate down at the rate of g 6

mass density and a length L 3m Its two ends are D 2m apart Two blocks of mass M 8 kg each are suspended from the string as shown in the figure The time taken by a wave pulse to travel from point A to point B is T A M T B M L

3 In Fig 6 37 a block of mass m 5 0 kg is at rest on a ramp The coefficient of static friction between the block and ramp is not known Find the magnitude of the net force exerted by the ramp on the block 0 m Figure 6 37 Problem 13

vi Block C shown in figure 1 72 starts from rest and moves downward with a constant acceleration Knowing that after 12 s the velocity of block A 7 2 m s determine the acceleration of A B and C and the velocity and the displacement of block p after 8 s B Figure 1 72

M AP Figure 1 2L X Figure 2 Note Figure not drawn to scale 15 A block of mass Mis suspended from two identical springs of negligible mass spring constant kand unstretched length L First one spring is attached to the end of the other spring The block is then attached to the end of the second spring and slowly lowered to its equilibrium position The two springs stretch a total distance of X as shown in Figure 1 above Next the springs are hung side by side The block is attached to the end of the springs and again ively lowered to its equilibrium position The springs each stretch a distance of X as shown in Figure 2 above Which of the following equations correctly shows the relationship between X and X A X X B X 2X L X C X 2X D X 4X

A bead is free to slide down on a smooth wire rightly stretched between points A and B on a vertical circle of radius 10 m Find the time taken by the bead to reach point B if the bead slides from rest from the highest point B A on the circle 0 C

18 A man of mass 60 kg is pulling a mass M by an inextensible light rope passing through a smooth and massless pulley as shown in figure The coefficient of friction between the man and the The maximum value of M that can ground is u 2 be pulled by the man without slipping on the ground is approximately a 51 kg b 26 kg 60 G M c 46 kq 777 d 33 ka

23 A 2 kg block is connected with two springs of force constants k 100 N m and k 300 N m as shown in figure The block is released from rest with the springs unstretched The acceleration of the block in its lowest position is g 10 m s a zero b 10 m s upwards c 10 m s downwards d 5 m s upwards llllllll K 2kg K

16 In the arrangement shown in figure wedge of mass M All moves towards left with an acceleration a surfaces are smooth The acceleration of mass m relative to wedge is a a 2 c 2 M m a m M m 60 b d 2Ma m M m a m