Newton's law of motion Questions and Answers

18 The transverse displacement of a string clamped at its both ends is given by 2TX 3 y 0 06 sin cos 120rt where x and y are in metre and t is in second The length of the string is 1 5 m and its mass is 3 x 10 2 kg The tension in string is NCERT XI Pg 392 1 324 N 2 648 N 3 832 N 4 972 N CAMERA 1 Maximum displacement and max pressure 2 Minimum displacement and min pressure change 3 Minimum displacement and maxi pressure change 4 Maximum displacement and maxi pressure change 20 Newton assumed that sound propagatio a gas takes under NCERT XI Pg 1 Isothermal condition 2 Adiabatic cond 2021 07 31 00 05

Two identical pith balls are charged by rubbing against each other They are suspended from a horizontal rod through two strings of length 20 cm each the separation between the suspension points being points being 5 cm 5 cm In equilibrium the separation between the balls is 3 cm Find the mass of each ball and the tension in the strings The charge on each ball has a magnitude 2 0 108 C

1 A body of mass 60 g is kept on an inclined plane of inclination 30 If the downward resultant force is 0 1764 N estimate the value of the coefficient of 0 23 friction indicar

The cart is restricted to move down with an acceleration 2 m s There is no friction between the crate and the cart The mass of crate is 10 kg g 10 ms Crate Cart The normal force exerted by the cart on the crate is 90N The acceleration of the crate is 1 m s vertically The acceleration of the crate is 1 m s horizontally The work done by pseudo force on the crate is zero with respect to cart huom 30 2m s

A box of mass m slides without friction on an inclined plane On the box and perpendicular to the ceiling of the box there is a standing massless rod A bob of mass m is connected to the upper edge of the rod by a massless thread see figure The angle of the inclined plane is a The mass m is at rest relative to the box a state of equilibrium Let be the length of the thread A mass m is connected to the box by a pulley The angle between the thread and the rod is a and B are in radians Value of is A 3 B 6 v constant m C 2 m D 4

A man in a lift ascending with an acceleration throws a ball vertically up with a velocity u and catches it after time Afterwards when the lift is descending with the same acceleration the man again throws a ball vertically up with the same velocity and catches it after time 1 The velocity of projection of ball is 8442 2 1 1 84 4 4 B 81 1 1 1 C 841 2 1 1 D

Consider a power line between two poles the distance between the poles is L the linear mass density of the wire is u and the middle point of the wire hangs below the horizontal level at which the wire is xed to the poles by a distance d Assume that d L The tension T at the mid point of the wire L g Find n nd

kg each are 3 Two blocks A connected by a light thread which passes over a massless pulley as shown Both the blocks lie on wedge and both the blocks to be always in contact with the of mass m Assume friction to be absent everywhere is pulled towards right with constant acceleration a wedge The wedge lying over smooth horizontal surface g is acceleration due to gravity A m 37 m B 53 i Find the normal reaction acting on block A ii Find the normal reaction acting on block B iii Find the accelerations of block A and block B w t wedge iv Find the maximum value of acceleration a for which normal reactions acting on the block A and

At any given instant of time the frame of reference with respect to which the position of the object is described in terms of position coordinates x y z i e distances of the given position of an object along the x y and z axes is called

4 24 5 ms 5 A force F is applied to the initially stationary cart The variation of force with time is shown in the figure The speed of cart at t 5 sec is 50 F N 1 10 m s 3 2 m s 10 kg t s 5 F Parabolic 2 8 33 m s 4 Zero

In the system shown in figure the mass 30 kg pulled by a force of 200 N At the instant when it acceleration is 7 m s2 in forward direction what magnitude of acceleration of 15 kg mass 7 ms 15 mmmmmmmmm 30 200 N 2 0 66 m s 4 366 m s 1 1 6 m s 3 19 m s

63 The v t graph of a moving object is given in figure The maximum acceleration is Velocity cm sec 80 60 40 20 a 1cm sec c c 3 cm sec 2 10 20 30 40 50 60 70 80 Time sec b 2cm sec2 d 6 cm sec 2

t s Ratio of magnitude of net force acting on a stone of mass 0 1 kg just after it is dropped from win dow of a stationary train to that just after it is dropped from that of a train accelerating at a is 1 g g a 2 g g a2 1 2 3

Tarzan who weighs 600N swings from a cliff at the end of a vine 14 m long From the top of the cliff to the bottom of the swing he descends by 3 4 m The vine will break if th force on it exceeds 900 N Does the vine break O O No Yes The data is not enough to calculate the result

For Example If first third and fourth are the ONLY three correct options for a question with second option being an incorrect option selecting only all the three correct options will result in 4 marks Selecting only two of the three correct options e g the first and fourth options without selecting any incorrect option second option in this case will result in 2 marks Selecting only one of the three correct options either first or third or fourth option without selecting any incorrect option second option in this case will result in 1 marks Selecting any incorrect option s second option in this case with or without selection of any correct option s will result in 2 marks A fixed re coilless cannon fires a shell with a speed at the same instant a man falls from rest from point O The shell hits a point on the wall Initially shell is aimed towards a point P as shown in figure Mark the correct option s The falling man sees the shell move along straight line directed along initial velocity

A solid sphere of mass 10 kg is placed over two smooth inclined planes as shown in figure The normal reactions at 2 is 10x N Find x g 10 m s faangur fa 2 10x N 10k Enter your answer 10 m s 60 2 30

A stone is thrown from ground level over horizontal ground It just c three walls the successive distances between them being r and 2r inner wall is 15 7 times as high as the outer walls which are equal in height The total horizontal range is nr where n is an integer Find n

3 2 Acceleration due to gravity at surface of a planet is equal to that at surface of earth and density is 1 5 times that of earth If radius of earth is R radius of planet is 3 1 R 3 94 R 2 4 2 3 face of earth When the

A soap bubble with a radius r is placed on another bubble with a radius R figure Angles between the films at the points of contact will be 1 120 2 30 3 450 4 90

Two persons A and B of masses m and standing at two ends of flatbed stationary trolley of mass M on a smooth horizontal surface as shown below When the person standing at A jumps from the trolley towards left with velocity u with respect to trolley then Ac m B

Time s OR ples of each i An object of mass 200 kg is accelerated uniformly from a velocity of 5 ms to 15 ms in 5 s Calcula What are balanced and unbalanced forces Give exam FF FOR the change in the momentum of the object and also find the force acting on it

or Problems In the arrangement shown in figure all pulleys are smooth and massless When the system is released from the rest acceleration of blocks 2 and 3 relative to 1 are 1 ms downwards and 5 ms downwards respectively Acceleration of block 3 relative to 4 is zero 15 Find the absolute acceleration of block 1 1 2 ms2upwards 2 1 ms downwards 3 3 ms2 upwards 15 ms downwards 2 3

A player caught a cricket ball of mass 150 gram moving at a rate of 20 m s If the catching process be completed in 0 1 s then the force of exerted by the ball on the hands of the player is A B C 0 3 N 30 N 300 N 3000 N

Multiple Choice Type Questions 5x1 1 A force F is applied on the spring balance as shown in the figure given below The reading of A and respectively will be 1 FF F NF N 22 3 F 2 B 2 F F F 4 F 2 A F

b ANSWER PLEASE for the given composite lamina the breadth b of the rectangle is 18 mm the height h of the triangle is 22 mm and the length I of the rectangle is 40 mm Then coordinate of the centroid of the composite lamina is Moment of Inertia of the rectangle about the centroidal horizontal axis of the composite lamina is Moment of Inertia of the triangle about the centroidal horizontal axis of the composite lamina is Moment of Inertia of the composite lamina about its centroidal horizontal axis is mm with respect to the given origin O mm mm mm

Two blocks of masses 3m and m respectively a connected by a massless and inextensible strim The whole system is suspended by a massle spring as shown in figure The magnitudes acceleration of A and B immediately after the sprin is cut are respectively fundigenl 3m A B C D g g 3 3 2013 g 8 g 5 8

A block of mass 1 kg is stationary with respect to a conveyor belt that is accelerating with 1 m s upwards at an angle of 30 as shown in figure What can be the coefficient of static friction between the block and the belt 0 4 0 6 0 8 01 0 Z 30 4

Due to the application of a force on a body of mass 100 kg that is initially at rest the body moves with an acceleration of 20ms in the direction of the force Find the magnitude of the force Ans 2000N

4 4 A man is dragging a trunk a trunk up the loading ramp of a mover s truck The ramp has a slope angle of 20 0 and the man pulls upward with a force F whose direction makes an angle of 30 0 75 0 with the ramp Fig E4 4 a How large a force F is necessary for component F parallel to the ramp to be 90 0 N b How large will component Fy perpendicular to the ramp be then

A neutron having kinetic energy 13 6 eV collides with a hydrogen atom in ground state at rest Assume that the mass of neutron and hydrogen atoms are same and the neutron does not leave its line of motion Then which of the following is the possible KE of the neutron after the collision A zero skipped B C D 3 4 eV 1 5 eV 6 8 eV Str

Two blocks A and B of masses 4 kg and 6 kg are connected by spring of unknown spring constant There are no external forces in horizontal direction on the system containing A B and spring If at a moment acceleration of B is 1 5 m s leftward and magnitude of acceleration of A is a m s2 Find a A mooooo 1 5m s B

A block of mass m is placed in contact with one end of a smooth tube of mass M see figure A horizontal force F acts on the tube in each case i and ii Then mark incorrect option M A a 0 and a C a am F M F M m in i in ii M i 8 a a F M m in i mF M m D Force on mis in ii

P 4 55 CP CALC A block of mass 2 00 kg is initially at rest at x on a slippery horizontal surface for which there is no friction Starting at time 0 a horizontal force F t B at is applied to the block where a 6 00 N s anwd B 4 00 N a What is the largest positive value of x reached by the block How long does it take the block to reach this point starting from 7 0 and what is the magnitude of the force when the block is at this value of x b How long from 0 does it take the block to return to x 0 and what is its speed at this point HERE P

In figure if 0 1 is the coefficient of friction between the wedge and the horizontal surface then for what maximum value of m in kg the wedge remains at rest take M 18 kg and 0 45 1 D smooth M In

10 Two beetles are hanging from the lower end of a light elastic cord suspended from the ceiling Stiffness of the cord is k its relaxed length is lo mass of each beetle is m and acceleration due to gravity is g One of the beetles starts climbing the cord with a constant velocity u relative to the ceiling while the other one keeps on hanging from the lower end With what velocity and in which direction will the lower beetle be shifted Ignore all disturbances caused by the initial acceleration of the beetle that is climbing the rope

Figure shows an ideal pulley block of mass m 1 kg resting on a rough ground with friction coefficient 1 5 Another block of mass M 11 kg is hanging as shown When system is released it is found that the magnitude of acceleration of point P on string is a Find value of 4a in m s Use g 10 m s m lkg 1 5 M I

A 25 kgf weight P is held in equilibrium by two strings which run over two pulleys Counterbalances Q and R are attached to free ends of the strings One of the counterbalances weighs 20 kgf the sine of the angle formed by the string and the vertical is 0 6 Neglecting friction of the pulleys determine the weight R of the other counterbalance and the angle a formed by the second string with the vertical The weight of the strings may be neglected A 20 kg 53 B 20 kg 37 P B C 15 kg 37 D 15 kg 53

In the figure shown pulleys and string are ideal The system is at rest Suddenly block p is mparted an impulse of 5 N S downwards What is the resulting motion of the system Take mass of p 2kg A p moves downwards with a constant speed of 5 m s B Both p and p move downwards with a constant speed of 5 m s C p moves downwards with a constant speed of 3 75 m s D p moves upwards with a constant speed of 2 5m s P B P

D A block is given an initial velocity of 38 m s up an incline of angle 37 The coefficient of friction between the block and the inclined surface is 0 2 How much time does the block take to stop Assume g 10 m s 38 m s

A particle is moving on x y plane so that its position Vector varies with time as r 10 3ti 10t t If initial velocity of particle is inclined at angle 8 from vertical then 8 is 1 30 2 45 3 60 4 tan 2 1 3

A long horizontal insulating cylinder of radius R and length L is free to rotate about its axis Curved surface of the cylinder carries charge Q which is uniformly distributed over it A string is wrapped around the cylinder at the end of which a point like mass m is hung The mass m start falling causing the cylinder to revoive about its axis Neglect moment of inertia of the cylinder 16 Torque on the cylinder due to electric field produced by charge on its surface is 4 Q Rg A H Q Rg L H Q Rg 4TL 1 H Q 47Lm B D L 1 H Q 4xLm H Q Rg 4TL

Consider the shown arrangement where the blocks A and B connected by means of a uniform string is being moved vertically up by the force F Each block weighs 2 kg while the mass of string is 500 gm The tension at midpoint of the string equals F 54N A B 201

1 In the diagram shown assume the pulley is smooth and fixed and the ropes are massless The mass of each block is marked on the block in the diagram Assume g 10 m s Find the magnitude of the acceleration of block M immediately after the system is released from rest LLU 74

A table with smooth horizontal surface is turning atan angular speed about its axis A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre Find the speed of the particle with respect to the table as its distance from the centre becomes L O r m

In planar polar co ordinates an object s position at time is given as t r 0 e m 81 rad a Find radial velocity tangential velocity and speed of particle at t 0 b Find radial acceleration tangential acceleration and magnitude of acceleration at t 0

25 Ambala is at a distance of 200 km from Delhi Ram sets out from Ambala at a speed of 60 km h and Sham set out at the same time from Delhi at a speed of 40 km h When will they meet

A chain of mass 10 kg and length 10 m is resting on a rough horizontal surface 0 2 A constant force of 30 newton is applied at one end The tension in the mid point of the chain is 1 20 N 2 15 N 3 10N 4 5NO

1 29 A body of mass m is thrown straight up with a velocity uo Find the velocity u with which the body comes down if the air drag equals cu where c is a constant and u is the velocity of the body Ans u 1 uo 2 cuo mg 1 2

5 A uniform rod has a weight of 40 N and a length of 1 m It is hinged to a wall at the left end and held in a horizontal position by a vertical massless string at the right end What is the force in the string 1 5 N 3 20 N Hinge Wall Rod String 2 10 N 4 40 N

A block of mass 2 kg is kept on a horizontal floor The coefficient of friction between the floor and the block is 0 2 A force F i 31 N acts on the block which is constrained to move along the x direction What will be the force of friction in N acting on the block Take g 10 m s A 11 B 11 3 4