Newton's law of motion Questions and Answers

Consider the system shown in figure Assuming string and pulley are ideal and coefficient of friction for all contacts is 0 2 calculate minimum force F for which the wedge will move towards right tan 37 g 10m s 12 N 15 2 N 24 N 4kg 2 kg 370 A

prin constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h see the figure Initially the spring makes an angle of 37 with the vertical when the system is released from rest The speed of the ring when the spring becomes vertical ILL E h k 1 37 ooooo 2 h m

A homogeneous flexible rope rests on a wedge whose side edges make angles a and B with the horizontal refer figure The central part of BC the rope lies on the upper rib C of the wedge With what acceleration should the wedge be pulled to the left along the horizontal plane in order to prevent the displacement of the rope with respect to the wedge Consider all surfaces to be smooth C

12 5 men each of mass 100 kg are travelling in different cars as shown Choose the correct alternative s 5m s A B 5m s C 5m s 1 pseudo force on A as seen by B will be 500 N 2 pseudo force on C as seen by B will be 500 2 N 3 pseudo force on D as seen by B will be 1000 N 4 pseudo force on B as seen by E will be 1000 N 5m s D E 5m s

Is Sta a st are made up person of pulley strings platform is shown in figure The force exerted by the person on the rope so that the system remains is equilibrium is 1 mg 3 m M M m M M 2 m M M g 4 Nona Toy

A cube of mass M starts at rest from point 1 at a height 4R where R is the radius of the circular track The cube slides down the frictionless track and around the loop The force which the track exerts on the cube at point 2 is 1 Question Type Single Correct Type 2 3 3 mg mg 4R 2 mg R

If friction is present between A B only and applie force is greater than limiting friction Find the tim after which body A will fall off from B 1 3 F A m L M 2L B 2mML MF mg m M 2 4 2L Hg 2mML

37 A man of mass m climbs up along massless rope with an acceleration of The force of contact 2 between block and ground is Mass of block 3m 1 3 mg 2 5 ma 3m a g 2 2 mg 2 4 mg

Referring to figure a and b 6kg a Spring balance 2kg 4kg kulged b 4kg reading of spring balance in a is 8 g and in b is also 8 g reading of spring balance in a is 8 g and in b it is less than 8 g reading in a is less than 8 g and in b it is 8 g reading in both lo and b in logo ther a

15 m s A 5 N B 10 N Before C 20 N D 25 N E 50 N 10 m s A 0 060 kg tennis ball moving at 15 m s strikes a tennis racket and rebounds at 10 m s in the opposite direction as shown above The ball is in contact with the racket for 0 030 s After 33 What is the magnitude of the average force exerted by the racket on the ball Isage Purcha

13 To study effect of air resistance a rubber ball was shot vert upwards from a spring gun from 20th floor of a tall building Veloc the ball was recorded at regular intervals of time and the data obta were plotted on a graph paper Some of the marking on the axe erased as shown in the following figure With what speed did the strike the ground v m s 0 2 t s

Comprehension for Q No 39 Q No 40 As shown in fig the weight W is 60 N and it is in equilibrium Then answer the following questions 40 F1 90 45 W 90 F2 39 The tension in the diagonal string is approximately 1 60 N 2 90 N 3 85 N 4 100 N Find the magnitudes of the horizontal forces F and F that must be applied to hold the system in the position shown 175 N 90 N respectively 2 60 N 60 N respectively 00 respectively

A homogeneous ring of radius 0 2 m and mass 5kg rotates about its normal axis Angular velocity of the ring as a function of time is given byw 3 5t rads The tangential force applied to the ring is

A particle started from rest and traverses a distance 2x with uniform acceleration then moves formly over a further distance 4x and finally comes to rest after moving a further distance 6x L uniform retardation Assuming entire motion to be rectilinear motion the ratio of average speec 3 the journey to maximum speed on its way is where n is n 1 5 2 4 3 3 4 2

27 If the ratio of lengths radii and Young s modulii of steel and brass wires in the figure are a b and c respectively Then the corresponding ratio of increase in their lengths would be 2a c b 2ac 6 a c b d 3a 26 c 3c 2ab EM Steel Brass 2M

In a particle accelerator a beam of proton is emitted at 1 5 x 107ms 1 The beam of some protons strike head on with gas atoms and rebound at 1 2 107ms If the initial velocity of gas atom is negligible find the mass of gas atom in terms of mass of proton Assume mass of proton is m

Two masses A and B of mass 4 kg and 1 kg respectively are connected with the help of massless inextensible string Mass A is placed on a rough horizontal table and mass B is hanging with the help of string passing through a smooth hole at the centre of table For the system to be in equilibrium what can be the minimum value of coefficient of friction 1 0 5 3 2 5 2 0 25 4 0 125

An object of mass 500g initially at rest acted upon by a variable force whose X component varies with x in the manner shown The velocities of the object at point X 8 m and X 12 m would be the respective values of nearly isF N qy 201 10 10t 201 25 1 boils 4 5 8 10 12 1 18 m s and 24 4 m s 2 23 m s and 24 4 m s 3 23 m s and 20 6 m s 1 18 m s and 20 6 m s x m g 6

A horizontal frictionless rod is threaded through a bead of mass m The length of the cart is L and the radius of the bead r is very small in comparison with L r L Initially at t 0 the bead is at the right edge of the cart The cart is struck and as a result it moves with velocity Do When the bead collides with the cart s walls the collisions are always completely elastic Given m M 13 14 C What is the velocity of the cart after the first collision in the center of mass frame m vo Mvo A B A m M M m M m C DO D L The first collision takes place at time t1 and the second collision takes place at t 0 till t t if m Mo 2ML m M 2M B M m M 2M m M D L ML 2 m M ML 2 m M m

Q10 Figure shows two cases In first case a spring spring constant K is pulled by two equal and opposite forces F at both ends and in second case is pulled by a force F at one end Extensions x in the springs will be FmF vom F a in both cases x b In both cases x c in first case x in second case x d In first case x in second

Two blocks lie on each other and connected to a spring as shown in figure What should be the mass of blocks A placed on block B of mass 6 kg so that the system s period is 0 75 s Assume no slipping what should be the minimum value of coefficient of static friction u for which block A will not slip relative to block B if block B is displaced 50 mm from equilibrium position and released k 600 N m moo A m kg s B 6 kg MH2

Given in the figure are two blocks A and B of weight 20 N and 100 N respectively These are being pressed against a wall by a force F as shown If the coefficient of friction between the blocks is 0 1 and between block B and the wall is 0 15 the friction force applied by the wall on block B is FA B

3 A where the string B TT A pendulum of mass m is connected to the ceiling of a car which in turns moving with constant acceleration a on horizontal ground Pendulum is at rest with respect to car There are two observers A sitting in car and B is on ground at rest Based on above information choose correct option is tension force on mass by

Q5 A mass M is placed on a very smooth wedge resting on a surface without friction Once the the mass is released the acceleration to be given to the wedge so that M remains at rest is a where CBSE AIPMT 1998 M a a is applied to the left and a gtane b a is applied to the right and a gtand c a is applied to the left and a gsing d a is applied to the left and a acose

6 Pratish weighs 588 N and is weightless onboard the International Space 10p Station ISS If she pushes off a wall with a vertical acceleration of 3 00 m s 2 determine the force exerted by the wall during her push off

23 A long flexible inextensible rope of uniform linear mass density A is being pulled on a rough floo with horizontal force F in such a way that its lower part is at rest and upper part moves wit constant speed v see Fig 13 The magnitude of F will be a 2 b Av Figure 13 INPHO 2009

3 2 In the figure shown all the surfaces are smooth The blocks A B and C have the same mass m F is floor and W is the wall 2mg cos 0 mg cos 20 1 sin 0 1 sin 0 If wall removed then find acceleration block B FI Find the magnitude of the contact force in newton between wall and block C A A C 2g sin 0 1 3sin 0 g sin 0 1 3sin 0 A B B C mg cos 0 1 cos 0 B 2gsin D W 2g sin 0 V1 sin 0 D mg sin 20 1 cos 0

Q4 When the block in the string is c M m m mm 1 g m m b d CBSE AIPMT m m g m m 2 mm 0 H g m m m A sliding B

2 The post is to be pulled out of the ground using two ropes A and B Rope A is subjected to a force of 6 kN and is directed at 60 from the horizontal If the resultant force acting on the post is to be 12 kN vertically upward determine the force T in rope B and the corresponding angle 0 T B A 60 6 0 kN

Q7 Man A of mass 60 kg pushes the other man B of mass 75 kg due to which man B starts moving with acceleration m s Calculate the acceleration of at that instant Smooth sugface a 4 15 m s b 15 4 m s c 4 21 m s d 21 4 m s 3m s B

M A wedge free to move of mass M has one face making an angle a with horizontal and is resting on a smooth rigid floor A particle of mass m hits the inclined face of the wedge with a horizontal velocity vo It is observed that the particle rebounds in vertical direction after impact Neglect friction between particle and the wedge take M 2m vo 10m s tana 2 g 10m s Assume that the inclined face of the wedge is sufficiently long so that the particle hits the same face once more during its downward motion Calculate the time elapsed between the two impacts

18 In the arrangement shown in figure coefficient 1 of friction between the two blocks is 2 The force of friction acting between the two blocks is N 2 10 200 F 2N 1 8 N 3 6 N F 20N 777 2kg 4kg Smooth Ju 1 1 2 b sma 2 10 N 4 4 N

Q6 In the adjoining figure a wedge is fixes to an elevator moving upwards with a acceleration a A block of mass m is place over the wedge Find the acceleration c the block with respect to wedge Neglec friction m a gsine b g a sini c g a sine d g a tane

no work is done on moving a block uniformly on smooth horizontal table INCORRECT work done by earth s gravitational force on moor zero considering moon s orbit to be circular no work is done by weight lifter holding a 175 kg mass steadily on his shoulder for 30 s

7 A chain of mass M and length L is suspended with both ends attached to ceiling Then one end is set free and chain starts falling as shown in figure The force on the ceiling as the function of x is www 1 Mg 2 2 i L 5x 2 Mg L 3x L 2 L x 3 Mg 2x X 28 Hin

Inextensible The string and the pulley are light The bob is released and the string starts wrapping around the pulley The pulley is held in place by a force applied at the centre m A r NTA Abhyas Test Chapter wise Questions YOUT For more free study materials visit www mathongo com or download the MathonGo app Find the rate r at which the length of the string wrapped around the pulley increases as a function of 9 R L Re 2g l Re sine R Doll RAlsing R 1 sin Al B BY 2g 1 Re sine Rcost Work Power and En

A body of mass 32 kg is suspended by a spring balance from the roof of a vertically operating lift and going downward from rest At the instant the lift has covered 20 m and 50 m the spring balance showed 30 kg and 36 kg respectively Then the velocity of the lift is 1 decreasing at 20 m and increasing at 50 m 2 increasing at 20 m and decreasing at 50 m 3 continuously decreasing at a steady rate throughout the journey 4 constantly increasing at constant rate the journey

stration 24 A block slides down a smooth inclined plane when released from the top while another falls freely same point Which one of them will strike the ground a earlier b with greater speed

2 10 A man with mass 85 kg stands on a platform with mass 25 kg He pulls on the free end of a rope that runs over a pulley on the ceiling and has its other end fastened to the platform The mass of the rope and the mass of the pulley can be neglected and the pulley is frictionless With what force does he have to pull so that he and the platform have an upward acceleration of 2 2 m s Take g 10 m s Ans 15 N 270 NJ 11

A sphere of radius R comes in contact with wedge moving as shown The point of contact is R 5 from the ground as shown in the figure Velocity of wedge is 20 m s then the velocity of the sphere at this instant will be A 20 m s B 10 m s 20m s R 5 C 5 m s D 15 m s

93 A block of 8kg acted by a force of 56N exerted by a string in vertically upward direction as shown The system starts from rest Find the work done by tension in 1st 10 seconds 56N 8Kg

pase of g As with res a on of less and Ans 19g 29 17g 29 21g 29 2 8 A smooth ring A mass m can slide on a fixed horizontal rod A string tied to the ring passes over a fixed pulley B and carries a block C of mass M 2m as shown in figure 2 198 At an instant the string between the ring and the pulley makes an angle a with the rod a Show that if the ring slides with a speed v the block descends with speed vcosa b With what acceleration will the ring start moving if the system is released from rest with a 30 m Ba B M Figure 2 198

Two blocks with masses m 3kg and m 5kg are connected by a light string that slides over a frictionless pulley as shown in figure Initially m is held 5m above the floor while mais on the floor The system is then released Find the speed at which m hit the floor g 10 m s 10m s or m m 5m 2 7m s

2 6 A particle of mass M is dropped vertically into a medium that offers resistance proportional to the velocity of the particle The buoyancy of the medium is negligible and the resisting force per unit velocity is f What uniform velocity will the particle finally attain Ans Mg T

5 The axle of a pulley of mass m 1 kg is attached to the end of a spring of spring constant k 200 N m whose other end is fixed to the ceiling A rope of negligible mass is placed on the pulley such that its left end is fixed to the ground and its right end is hanging freely from the pulley which is at rest in equilibrium We begin to pull the endpoint A at the right end of the rope by a constant vertical force of F 15 N Friction can be neglected between the rope and the pulley Find the maximum displacement of point A after applying F Express your answer in cm Imm m

A massless spring when stretched by a force 150N shows an extension of 1 5m This spring is arranged as shown in figure A block of mass 10kg is released at rest on a frictionless incline It slides down and compresses the spring by 3m before coming to rest momentarily Distance by which the block slides before hitting the spring is 1 4m 10Kg 0 30 Foooo 2 6m 4 12m

There is no friction anywhere and the blocks hav an instantaneous velocity vo in the position Fin the instantaneous power supplied by m to m 1 3 m F m m m m m V 0 2 FV0 2 FV 4 m F m m Vo

37 In the figure shown all the surfaces are smooth and pulleys are light and frictionless Masses of A B and Care 9m 2m and m respectively All contacts are smooth and string is massless and 0 tan 64 3 Acceleration of C is nearly equal to take g 10 m s 9 A 9 m sec B 4 5 m sec A B C 3 m sec D 7 5 m sec

A uniform chain has mass M and length L It is placed on a frictionless table with length 1 hanging over the edge The chain begins to slide down Then the speed v with which the chain falls when the entire length of chain just becomes vertical is 1 v L 1 3L 3 V L b 2 v 1 13 V 4 v 2g L 1

2 3 A baseball is dropped from the roof of a tall building As the ball falls the air exerts a drag force that varies directly with the speed as f qv is a constant Show that the ball acquires a terminal speed Find the speed of the falling ball as a function of time mg Ans 1 e qum