Newton's law of motion Questions and Answers

11 A sphere of mass M 3 kg and radius R 0 1 m is held in place against a wall by massless string connected to the wall at an angle 0 37 from the vertical The string connects to the sphere tangentially as shown in the figure What is the magnitude of the normal force in newton provided by the wall 5 R R

A block of mass 4 kg is moving on a rough horizontal surface with constant velocity 10 m s as shown in figure The contact force exerted by the surface on the block is g 10 m s 1 30 N 2 40 N 350 N 4 100 N 10 m s 4 kg 30 N 30 40 end N 40 N

under gravity at an angular position a with vertical upward direction The rod makes inelastic impact with the smooth ground at end A Just after impact 1 Acceleration of centre of mass is 3 sin 1 3 sin a g AX g 2 Acceleration of centre of mass is sin a 1 3 sin 1 a 3 The acceleration of end A is 4 The acceleratio 3g sina cosa i 1 3 sin a sing cosa

pring is ed The g comes m The ed of 9 A block of mass m is pushed towards a movable wedge of mass 2m and height h with a velocity u All surfaces are smooth The minimum value of u for which the block will reach the top of the wedge is a 2 gh h 2m b 3gh 0 c 6gh m d gh

1 The system is released from rest from the position shown in the diagram If A and B have mass m and M respectively and all surfaces are smooth then the normal reaction between A and B is string and pulley are massless 3m 1 2Mm M m 2 T Mmg 2 M m B 3 Mmg M m STAFFRETER 52 10 10x4 1x10x 254 Hot 10 224 2 2 ze zero kwU

A block of metal weighing 2 kg is resting on the frictionles plane It is stuck by a jet releasing water at the rate of 1 k s and with a speed of 5 m s 1 The initial acceleration o block is O2ms O 2 5 m s

A 0 621 kg ball initially moving with a speed of 2 73 m s bounces off a wall and then moves with a speed magnitude half of its original directed in the opposite direction If the ball is in contact with the wall for 6 ms what is the magnitude of the average force that the wall exerts on the ball Express your answer in two decimal places in Newtons

The uniform square plate of mass 6 kg is placed on the x y plane If a horizontal force P 12N is applied to one corner in the direction shown Initial acceleration of point A is a m s Fill the value of A P 45 B is smallest possible integer 2

1 3 The force of contact between ball and wall increases linearly from zero to F in time A ball of mass m moving with speed u collides with a wall normally and returns with spe emains constant for next T 3 time and decreases linearly to zero in further T 3 time Va B 2mu 3T C mu T D 2mu T

n the given figure system released from res and bead starts sliding vertically downwar with the acceleration 3m s 2 with respect o rope find the acceleration of block A unattempted In the given figure system released from rest and beads acceleration 3m s2 w r to rope find acceleration of bloc f fax fara ftemmaten you fazer var 3m s al fhum qual 1 a IN T A 4kg bead of mass 2kg 13 A 3 m s 17 B 7 m s 4 C 2 m s D None of these

7 Which of the following sets of concurrent force may be in equilibrium 1 F 2 N F 5 N F3 9 N 2 F 3 N F 6 N F3 8 N 3 F 4 N F 6 N F3 12 N 4 F 5 N F 10 N F 4 N

A block of mass 4 kg lies over a horizontal surface g 10 m s 2 Another block of mass 2 kg is placed over the first block The normal reaction between the first block and ground surface is 1 40 N 3 20 N 2 60 N 4 10 N

A round table with four symmetrical pointed legs is lying over a horizontal surface If mass of the table is m then normal reaction of surface on each leg is equal to 1 2mg 3 mg 3 2 mg 4 4 mg 2

It is easier to draw up a wooden block along an inclined plane than to haul i vertically principally because a b d The friction is reduced The mass becomes smaller dwozg gedemo Only a part of the weight has to be overcome g becomes smaller

A 0 1 kg ball is dropped from a height h 1 m strikes the ground and bounces back a maximum height hr 0 8 m If the ball is in contact with the ground for t 0 01 s then the magnitude of the average force in N applied by the ground on the ball is O a 77 5 O b 102 3 O c 33 8 O d 4 7 O e 84 7 hi hf

A block of metal weighing 2 kg is resting on the frictionless plane It is stuck by a jet releasing water at the rate of 1 kg s and with a speed of 5 m s 1 The initial acceleration of block is 2 2 5 m s 2 4 3 5 m s 2 1 2 ms 3 3 m s

A uniform rope of mass m and length is spread out on a horizontal frictionless surface wrapping half turn around a fixed vertical frictionless cylinder of radius 1 Initially both the ends of the rope are pulled by equal forces each F in magnitude keeping both the unwrapped segments parallel to each other and equal in length as shown in the figure Suddenly pulling force at one end is removed without any change in the pulling force at the other end After how much time from removal of the pulling force at an end will the rope start losing contact with the cylinder F f

31 A man of mass 50 kg is standing on an elevator If the elevator due to some technical failure starts to fall freely under gravity then the apparent weight of the man becomes a 490 N b 50 kg czero d greater than 490 N

Wedge is accelerating right such that smaller block does not slide on wedge Work done by total normal force on wedge in some time is m danguP FROM 9 1090 10990

Three identical cylinders each of mass m 10 3 kg are arranged on a horizontal floor as shown in the figure with their axes horizontal The floor as well as the cylinders are frictionless You apply a constant horizontal force directed to the right on the left cylinder For what range of F will all three cylinders remain in contact with each other Acceleration of free is g 10m s F

A force F prevents a 2 kg brick from falling by pressing it against a vertical wall If the coefficient of static friction between the brick and the wall 0 5 what minimum force F in N must he use O a 25 O b 100 OC 20 O d 40 O e 50 F mg

1 15 N 10 N 2 25 N 5 3 10 N 25 N 4 5 N 25 N The magnitude of acceleration of blocks of mass 2 kg and 4 kg are a and a respectively Pulley and strings are massless and g 10 m s2 The is relation between a and a 1 a 2a 3 a 4a F 60 N G 2 kg 4 kg 2 2a a 4 a a

m 3 in N cord m2 See the figure The force Fo is 45 N The cord exerts equal but opposite forces on the two boxes The boxes slide without friction on the floor 16 67 Fo Calculate the tension force exerted by the cord Data m 13 kg m2 17 kg the mass of the cord is negligible 19 50oC 22 82 OD 26 69 OF 31 23 OF 36 54 06 42 75 OH 50 02

11 To allow the elastic string to become slack the minimum value of x is 2 L 3 4

A boy throws a ball vertically upward with a velocity vo 13 m s The maximum height reached by the ball in m is O a 5 O b 16 9 O c 8 5 O d 7 2 O e 9 8

Block of mass m is placed on smooth fixed wedge as shown When block is released normal contact force exerted by ground on wedge is A 7777 D M m cose g B M m sin 0 g M cos e m g M mcos 6 g M m 07 ts PHYSICS 0 Completed 6 2 7 3 9

A 4 kg block is sliding down a plane inclined at 30 with a constant velocity of 8 m s To determine the coefficient of friction between the block and the plane what pieces of information do you need Angle of slope The mass of the block only The mass of the block the angle of inclination The mass of the block the angle of inclination and the velocity

Problem 1 Two blocks of masses m and m can move freely on a platform The block with mass m is connected to a wall by a spring of spring constant k and the block with mass m is connected to m through another spring of spring constan K Find the equation of motion for each of the blocks

A block A of mass 50 kg is placed on the cart having mass 100 kg as shown in the figure and acceleration of the cart is 2 ms 2 If the pulley and strings are light and force of friction between the block and cart is 150 N and there is no sliding between the block and the cart then A O 50 kg 100 kg O MO a 2 ms 1 Force acting on the cart is 800 N 2 Force exerted by the pulley on the cart is

pulley system The friction in the system is negligible and gravity acts in the negative y direction Determine the magnitude of the tension in the ce Cart A 175 lb 9 09 lb 19 9 lb 15 9 lb G Cart B 100 lb Y P 75 lb

18 a Determine the moment of a 90 N force about point C for the condition 15 Also determine the value of 0 for which the moment about C is b zero and c a maximum see Figure 1 Q18 Ans a M 33 5 Nm b 36 9 or 21 7 c 126 9 or 307 600mm B 800mm 90N 0 A od t

21 Two objects having masses of M and 2M exert a gravitational force F on each other The distance between their centres is R Now the distance between their centres is made 4R and masses have been increased to 2M and 4M respectively Choose the option that correctly gives the gravitational force between masses of 2M and 4M A 0 25 F B 0 50 F C 0 75 F D 1 00 F

Blocks A and B are initially in equilibrium The springs and strings are ideal The of the blocks A and B just after the spring 2 is cut are accelerations respectively Spring 1 000000 2m B reeeeee Spring 2

What will be the speed of a 2 0 kg mass originally traveling at 3 0 m s that undergoes a time varying force in the same direction as the initial velocity as graphed below F N 4 3 2 1 4 0 m s 8 0 m s 7 0 m s 6 0 m s 4 5 m s 2 3 t s

40 A particle of mass 50gm is attached with a light string length 5m connected with a corner A of a fixed square frame ABCD of side 2m The whole system is placed on a frictionless table and appears as shown when seen fron the top The particle is given an initial velocity 2m s What is the distance in metres travelled by the particle till it hits the square frame 2m a 5 5 m c 6 5 T B 5m Av 2m s 50gm b 4 5 T d 9r

In the adjacent figure a uniform rod of mass m and length is rotating with a constant angular speed on a smooth horizontal surface about a fixed vertical axis perpendicular to its length and passing through one 3l end The tension at the point P at distance from the axis is found to 4 T Where To is the tension in the rod near the axis Find 2x 1 4x the value of x be T L 3l 4

Two pistons are inserted into a horizontal pipe with cross sectional area A and length 21 The left piston is connected to a wall by a spring with a force constant k Initially the left piston is at the end of the pipe and the right piston is in the middle of the pipe as shown The spring is relaxed and the pressure Pbetween the pistons equals the atmospheric pressure Then the right piston is slowly pulled to the right until it reaches the end of the pipe What force F must be applied to the piston to keep it in that position The pipe remains at rest Neglect friction and assume constant temperature 21

A cup having shape of a frustum of a cone is placed on a horizontal tabletop Mass of the cup is m 20g and diameter of its bottom is d 50 cm A uniform rod of mass M 10g is placed in the cup as shown The rod is inclined at an angle 0 60 to the horizontal Find maximum length of the rod in meter so that the system will not turn over T

0 16 Q 17 Q 18 A fireman wants to side down a rope The rope can Q 21 Two objects A and B of masses mA and mi attached by strings as shown in fig If they are g upward acceleration then the ratio of tension T hear a tension of th of the weight of the man With what minimum acceleration should the fireman slide down 1 2 A rope of mass 5 kg is moving vertically in vertical position with an upwards force of 100 N acting at the upper end and a downwards force of 70 N acting at the lower end The tension at midpoint of the rope is 2 85 N 1 100 N 3 75 N 4 105 N 1 1SF 3H6F A body is moving with a speed of I m s and a force F is needed to stop it in a distances If the speed of the body is 3 m s the force needed to stop it in the same distance will be My sin 0 2 3F 4 9F Masial 9 Q 19 Two blocks each having mass M rest on frictionless marfaces as shown in the figure If the pulleys are light and frictionless and M on the incline is allowed to movie down then the tension in the string will be Se freed ra 2 Me sin 0 4 2 My sin 12 Q 20 Two mines are hanging vertically over frictionless pulley The acceleration of the two masses is Q 22 Q 23 Q 24 1 mA mB mB 2 mA mBymA m m m m Me m A monkey of mass 20 kg is holding a vertical rope The rope can break when a mass of 25 kg is suspended from it What is the maximum acceleration with which the monkey can climb up along the rope 1 7 ms 2 10 ms 4 2 5ms 3 5 ms A body of mass 8 kg is hanging from another body of mass 12 kg The combination is being pulled by a string with an acceleration of 2 2 ms The tension T and T will be respectively use g 9 8m s 1 200 N 80 N 31240 N 96 N 12kg T the Sky 2 220 N 90 N 4 260 N 96 N At a given instant A is moving with velocity of 5 m upwards What is velocity of B at the time m Q

A light rigid rod is placed on a frictionless horizontal floor and blocks of mass of m and 3m are attached to the ends of the rod with the help of light inextensible cards If a horizontal force F is applied perpendicular to the rod at its midpoint as shown in the figure what will acceleration in m s2 of the midpoint of the rod be Take m 0 5 kg and F 12 N

Two masses A and B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table and B is held at the position shown Mass B is now gently lifted up to the pulley and allowed to fall from rest Determine up to what height will A rise for the ensuing motion 2m A B 1m

A projectile of 2 kg is launched from ground at an angle of 30 from horizontal At the highest point of its trajectory the radius of curvature is 16 km A Find its speed at highest point B Calculate its range on level ground C Calculate impulse due to gravity during total time of flight

Which of the following frames of reference inertial or noninertial should NOT be grouped with the rest a a satellite in Earth s orbit b a child on a merry go round c a parachutist in free fall d a person standing on a moving escalator e a baseball as it is being hit by a bat

24 A ball impinges directly on another ball at rest The first ball is brought to rest by the impact If half of the kinetic energy is lost by the impact the value of coefficient of restitution is od

An insect is trapped between two blocks of masses 3kg and 5kg placed on a smooth horizontal platform A force of 20N is first applied from the side 3kg and then from the side of 5kg block horizontally explain mathematically by drawing an appropriate free body diagram that from which side there is greater chance of survival of the insect 131

The figure shows an accelerometer a device for measuring the horizontal acceleration of cars and airplanes A ball is free to roll on a parabolic track described by t equation y x where both x and y are in meters A scale along the bottom is used to measure the ball s steady position x What is the acceleration of vehicle in if x 20 cm y x 0 5m 0m 0 5m

Q 16 54 A sphere of radius 5 cm and mass 4 kg rests on two point supports as shown such that the points A B and the centre of the sphere are in the same vertical plane Friction is absent The height difference between the supports and the centre of the sphere is shown in the figure The force in Newton acting on the sphere from the support A is g 10 m s 4 cm B 3 cm

Paragraph A block of mass Mis attached to an ideal spring of spring constant k and natural length L and placed on a horizontal frictionless surface with the othe end of the spring attached to a fixed support Initially the block is at rest and the spring is vertical and unstretched Now the block is suddenly given horizontal velocity v towards the right The block moves a distance 31 4 along the surface and then comes to rest The acceleration of the block at the instant it comes to rest is O O 3kL 20M 16M 7kL 120M kL 18 M

A sphere of radius 5 cm and mass 4 kg rests on two point supports as shown such that the points A B and the centre of the sphere are in the same vertical plane Friction is absent The height difference between g 10 m s the supports and the centre of the sphere is shown in the figure The force in Newton acting on the sphere from the support A is 4 cm B 3 cm

The initial velocity of ball A is 5 m s and then it hits balls B and C Ball B is driven at 2 8 m s in the direction shown Ball A leaves at an angle of 6 to the center of the line Find the velocities B and C The masses are ma 0 5 kg mb 0 30 kg and mc 0 35 kg VB 2 8 m s 50 V 5 m s B A C 6 40 Vc