Newton's law of motion Questions and Answers

etwork shown each resistance is equal to R The equivalent resistance between adjacent corners A and Dis A a R c R R 3 R R R b d 2 3 R R

6 A block of mass m is placed over a wedge of mass 4m and the system is acted upon by a horizontal force F Friction is absent everywhere The value of F so that the block does not slide over the wedge is 1 52 mg 3 4mg F 4m 30 Smooth 2 4 3 mg 5 mg 3

Five forces F1 F2 F3 F4 and F s are acting on a particle of mass 2 kg so that it is moving with 4 m s in east direction If F force is removed then the acceleration becomes 7 m s2 in north then the acceleration of the block if only F1 is acting will be 1 16 m s 3 260 m s 2 65 m s 4 33 m s

9 3 N t A block of mass m is sliding on a fixed inclined plane of angle 0 30 in case 1 In case II inclined plane is accelerated horizontally sa that the block does not slide with respect to it The ratio of acceleration of the block in horizontal direction in two cases is 30 Case 1 ao b 3 4 d 12 30 Case II

D Blocks A and B are kept on a plane inclined at an angle 8 with the horizontal Fig 2 45 Masses of blocks are m1 and m friction with the plane are and and coefficients of 1 respectively i Find the force between the blocks when they slide down and ii the minimum value of the angle Fig 2 45 for which the two blocks are about to slide down g 1 F 8 cost ii 0 tan m M A 0 B

1 In the given arrangement if the lift is moving g upwards with acceleration then force 2 exerted by the string on ceiling is 1 3 4mg 3 8mg 3 2m 127 2 3mg 4 4mg 5

In the arrangement shown in figure the relation between acceleration of blocks m and m is and 1 a a 3 a 3a2 m m a 2 2a a 4 3a a

The minimum value of coefficient of friction u such that block of mass 5 kg remains at rest is NCERT Pg 102 1 0 3 3 0 6 5 kg 2 0 5 4 0 4 3 kg

string pulley system as shown All the three masses are held at rest and then released To keep m3 at rest the condition is O 3 m m m 2 m3 1 m3 m m m m1 2 m3 4 m3 2m m m m 4m m m m 2

The position of a particle moving along X axis varies with time t as 4x 12 4 At what position the particle is at rest 1 x 4 3 x 1 2 x 2 4 X 2

A rocket is moving in a gravity free space with a constant acceleration of 2 ms 2 along x direction see figure The length of a chamber inside the rocket is 4 m A ball is thrown from the left end of the chamber in x direction with a speed of 0 3 ms relative to the rocket At the same time another ball is thrown in x direction with a speed of 0 2 ms from its right end relative to the rocket The time in seconds when the two balls hit each other is a 2 ms 2 0 3 ms 4 m 0 2 ms X

A nozzle throws a stream of gas against a wall with a velocity v much larger than the thermal agitation of the molecules The wall deflects the molecules without changing the magnitude of their velocity Also assume that the force exerted on the wall by the molecules is perpendicular to the wall This is not strictly true for a rough wall Find the force exerted on the wall IN AK A A nmv cos 0 C 2A nmv sin 0 B 2A nmv cos 0 D A nmv cos 0

Example 32 A mass of 6 kg is suspended by length 2 m from a ceiling A force of 50 N in the horizontal direction is applied at the midpoint of the rope as shown in Fig 5 29 What is the angle the rope makes with the vertical in equilibrium Take g 10 ms 2 Neglect mass of the rope NCERT 0 1 m T sin 0 T 0 1 m T cos e T T 6 kg wt T3 50 N

if m 20 kg m 20 kg m as shown in fig VA 300 N C 200 N 10 kg find normal force acting on the floor F ma Boja B 100 N D None of these TTT m2 m g 10m s 10 60

In Fig 6 343 man A is standing on a movable plank whil man B is standing on a stationary platform Both am pulling the string down such that the plank moves slowl up As a result of this the string slips through the hand of the men Find the ratio of length of the string that slip through the hands of A and B 5 27 F B A 2

If flat car is given an acceleration ao 2 m s starting from rest compute tension in the light inextensible string connected to block of mass 50 kg Neglect mass of pulley and its friction Coefficient of friction between block and flat car is 0 30 50 kg

COMPREHENSION V A 60 mm radius wheel is connected to a fixed support D by two links AB and BD At the instant shown the velocity of the centre A of the wheel is 30 m s to the left Rod AB and BD 30 m s have equal length 5 m 15 The angular velocity of rod AB will be A 3 2 rad sec C 7 2 rad sec B 5 2 rad sec D None of these 45 45 YOD 130

A uniform bar of length 3 m and mass 3 kg is as shown in the figure Tension at a point in the bar at 1 m from one end is 6 N 1 8 N 101 ON 1m 3 kg 3m 0 2 6 N 12 N 777

A rod of mass m and length e is hinged at point P and rod can rotate about hinge point P in vertical plane Other end of rod is connected through a block by a string which is passed through pulley of mass m and radius R and there is no slipping between the pulley and the string as shown in figure At t 0 system is released Find the hinge reaction at P at t 0 6 B A 12 11 C 4 11 mg mg D mg 11 8 11 mg m 2 m R 199990 m

jure If velocity of block A is 5 m s at given instant then velocity of block B in m s at the same instant is given by Given 0 60 6 37 B A In figure shown if the magnitude of acceleration of m is 2 N m s2 given that the string is inextensible and the acceleration of M is 2 m s towards left then find N m M

The minimum force necessary to pull up a body along a rough inclined surface is F But it becomes F when applied parallel to the inclined plane If is the coeffi cient of friction between the body and the inclined plane show that F F 1 4 inclination 30 are

c 3 5 m s d 4 m s 7 d Two bodies of mass in and 4 in are attached with string as shown in the figure The body of mass in hanging from a siring of length is executing oscillations of angular amplitude 0 while the other body is at rest The minimum coefficient of friction between the mass 4 in and the horizontal surface should be a c 2 cos00 3 1 4m COS 00 T T m 00 d Tieso Esimo 00 2 3 2 cos 0 b 2 cos

39 A block of mass m 2 kg is suspended with a light spring of spring constant k 1000 N m If the lift is moving vertically upward with acceleration of 2 m s2 then equilibrium elongation in the spring is g 10 m s heeeee 2 m s 1 3 44 The is ma

2 Two blocks A and B of mass 2m and respectively are connected to a spring of sprin constant k A horizontal force F 5mg is applie to block A as indicated If acceleration of block at the instant is g then acceleration of block A that instant is B moooooooAF 1 2g 2g 3 Smooth 2 3g 4 3g 77

A block A of mass MA 1 kg is kept on a smooth horizontal surface and attached by a light thread to another block B of mass Mg 2 kg Block B is resting on ground and thread and pulley are massless and frictionless A bullet of mass m 0 25 kg moving horizontally with velocity of u 200 m s penetrates through the block A and comes out with a velocity of 100 m s Find the height through which the block B will rise mm 25 kg 200 m s

The mass of a bucket full of water is 15 kg It is being pulled up from a 15m deep well Due to a hole in the bucket 6 kg water flows out of the bucket The work done in drawing the bucket out of the well will be g 10m s 1 900 JOE S 3 1800 J 2 1500 J 1 4 2100 J

Illustration 48 Two identical billiard balls strike a rigid wall with the same speed but at different angles and get reflected without any change in speed as shown in figure What is i the direction of the force on the wall due to each ball ii the ratio of the magnitudes of impulses imparted to the balls by the wall 4 L a 3 b 30 30 U

In the arrangement shown in figure pulley is massless and all the strings are light Let F be the force exerted on the pulley in case i and F the force in case ii Then 2 1 1 3 4m 2m F F F F 1 2 ii 2 4 4m m m F F F 2F

A monkey is climbing on the rope as shown in figure The string and the pulley are light The acceleration of monkey relative to rope is 2m s downwards The acceleration of the monkey is 11 NE 1 m s FIN 2 2 6m s 3 5m s2 4 zero 15Kg 15Kg plane whose inclinatio

Hilustration 26 The elevator shown in figure is descending with an acceleration of 2 m s2 The mass of the block A is 0 5 kg What force is exerted by the block A on the block B

Two masses M and M are connected by light string which passes over the top of a smooth plane inclined at 30 to the horizontal so that one mass rests on the plane and the other hangs vertically as shown in fig it is found that M hanging vertically can draw M up the full length of the plane in half the time in which M hanging vertically M draws M up Find Assume pulley to be smooth M 2 2 3 7 m 30

A ball is thrown vertically upward with some speed from the ground Ball passes a point h height above the ground at time 6 s and 10 s respectively The speed with which ball is thrown up from the ground is g 10 m s 1 60 m s 2 75 m s 3 80 m s 4 82 5 m s

A ball of mass 100g hits a smooth vertical wall normally with a speed of 15 m s four times per second and rebounds each time with a speed of 15 m s The average force exerted on the wall is 1 6N 3 30 N 2 15 N 4 12 N

The ratio of tension T and T is strings INCERT Pg 99 massless T 2 kg T 5 kg

39 Figure shows a weight of 30kg suspended at one end of cord and a weight of 70kg applied at other end of the cord passing over a pulley Neglecting weight of rope and pulley find the tension in the cord and acceleration of the system g 10ms 30kg H T T 70kg 1 2 m s 120 N 2 4 m s 420 N

Illustration 29 A particle of mass 0 3 kg is subjected to a force F kx with k 15 N m What will be its initia acceleration if it is released from a point x 20 cm

C 80 A block of mass 2 kg is suspended from a fixed support with the help of a uniform string of mass 1 kg and length 5 m Which of the following equation represents tension T in the string with distance x in meters from its lower end A T 20 N C T 2x 20 N B T 30 N D T 30 2x N M

A cylindrical pulley of mass M and radius R is connected to another cylindrical pulley of mass M 2 and radius R 2 through a massless string as shown in figure If sufficient string is wrapped over larger pulley find the acceleration of mass M attached to the smaller pulley when whole system is released from rest Assume there is no slipping in the smaller pulley RA

The blocks are of mass 2 kg shown is in equilibrium At t 0 right spring in figure and right string in figure ii breaks Find the ratio of of instantaneous acceleration of blocks 37 37 2kg B goooooo 25 C 37 37 2kg D 6

A rod AB of length 1m and mass m 2 kg is pinned to a vertical shaft and a massless string is tied with the shaft at the lower end of the rod length of the string ism as shown in figure If the shaft starts rotating with a constant angular velocity 5 rad sec Then find the tension in the string A 1 N C 3 N B 2N D ON shaft 3 5 m A

A body starts accelerating from rest under gravity What is the displacement of the body in the time interval of the 10 15 seconds Assume 2 g 10 ms 2

1 Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string The whole system is suspended by a massless spring as shown in figure The magnitudes of acceleration of A and B immediately after the string is cut are respectively g a g 3 b g g g d A3m Bm

A boy sitting on the topmost berth in the compartment of a train which is just going to stop on a railway station drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about 2 meter The apple will fall a Precisely on the hand of his brother b Slightly away from the hand of his brother in the di rection of motion of the train c Slightly away from the hand of his brother in the direction opposite to the direction of motion of the train d None of these A person sitting in an open car moving at constant veloc ity throws a ball vertically up into air The ball falls a Outside the car b In the car ahead of the person c In the car to the side of the person d Exactly in the hand which threw it up

9 The wedge is placed on a smooth surface and is being rotated about a vertical pole with angular speed w with the help of a string Over the wedge a block is placed and friction co efficient between them is 0 5 Find the maximum value of wo in rad sec for which the block does not skid up 1 10 2 2 3 5 9 20cm m 37 Rough Smooth

Example 5 21 Using constraint equations find the relation between Solution Points 1 2 3 and 4 are movable Let their displacements from a fixed lin X1 X2 X3 and x4 x x3 x x3 x4 X3 x x4 x x4 3 On double differentiating with respect to time we will get following three constraint relations a a3 0 a a4 2a3 0 a a 2a4 0 Solving Eqs i ii and iii we get a 7a Which is the desired relation between a and a2 ii iii a and 92 X Fig 5 73

the elect 1 Vo 2 3v 2 3 4V 3 6 The system shown in the figure is released from rest The masses of the wedges and the block are indicated There is no friction anywhere The wedge incline angle is 37 Take sin 37 3 5 Pulley is ideal and string inextensible For what value of M m will the smaller wedge of mass m not slip relative to the bigger wedge s inclined surface

The pulley A is smooth and fixed The pulley B is free to move and light The acceleration of m is a and that a a of m is a Find B H m 1 m s B 1 C 2 3 D 2

If two objects of masses 2 5 kg and 100 kg experience the same force 5 N what is the acceleration experienced by each of them

25 A block of mass m kg is kept on a weighing machine in an elevator If the elevator is retarding upward by a ms the reading of weighing machine is in kgf 1 mg 3 m 1 a 9 2 4 m g a m g a

24 The force acting on a particle moving along x axis varies with position on x axis as shown in figure O X X The particle is in stable equilibrium at 1 X X 2 X X 3 x 0