Newton's law of motion Questions and Answers

Three blocks with masses m 2m and 4m are connected by strings A and B as shown in figure After an upward force Fis applied on block m the masses are moving upward at constant speed v The tension in the string B will be AF m A 2m B 4m 7mg 6mg Zero hr min 4mg

27 An inclined plane makes an angle of 30 with the horizontal A groove OA 5 m cut in the plane makes an angle 30 with OX A short smooth cylinder is free to slide down under the influence of gravity The time taken by the cylinder to reach from A to O is g 10 m s a 4 s c 2 2 s JA 30 cylinder DA 30 b 2 s d 1 s

paper Two identical books each of n 400 pages are so meshed that their ROSTwo alternate papers overlap each other Mass of overlapped portion of each is m 0 5g and coefficient of static friction between the papers is u 0 1 The arrangement is placed on a frictionless horizontal table and the books are pulled apart horizontally without rotation Find minimum pulling force Frequired Acceleration due to gravity is g 10 m s F

In the diagram shown the larger block is being moved with an acceleration A 2g What is the acceleration of the 2m mass block with respect to the earth Assume no friction Strings are ideal 4 a Zero c 2g 3 b 4g 3 d None

8 In a two dimensional motion instantaneous speed V is a positive constant Then which of the following are necessarily true a The acceleration of the particle is zero b The acceleration of the particle is bounded c The acceleration of the particle is necessarily in the plane of motion d The particle must be undergoing a uniform circular motion

3 Assertion When a body is dropped or thrown from the same height it reaches the ground horizontally at the same time Reason They have same acceleration and same initial speed in vertical direction

does not change in time 9 A wagon of mass 2000 kg is separated from a train travelling at 9 km h and comes to the rest in 2 minutes What is the resistance between the wheels of the wagon and the track a 42 N c 45 N b 41 7 N d 47 N

he lever AB is welded to the bent rod BCD which is supported by bearings at E and F and by cable DG Knowing that the bearingat E does not exert any axial thrust determine a the tension in cable DG and b the reactions at E and F 24 4 cm 100 N E F 2 B C 16 cm 6 cm 6 cm D 25 4 cm 23 cm G 12 cm

A cannon standing on the top of a cliff 40 m high fires a cannon ball horizontally out to sea with a muzzle speed of 140 m sec How far out to sea does the ball go A 242 8 m B 262 8 m C 272 8 D 282 8 m nd necoloration a for time t and t

A person of mass 80 kg jumps from a height of 1 meter and foolishly forgets to buckle his knees as he lands His body decelerates over a distance of only one cm Calculate the total force on his legs during deceleration

12 A small bob attached to a string of length 1 is suspended from a rigid support and rotates with uniform speed along a circle in a horizontal plane Let be the angle made by the string with the vertical then the length of a simple pendulum having the same period is a cos 0 c sine b sine d cos 0

Two weights w and w rest on a rough plane inclined at an angle a to the horizontal and are connected by a string which lies along the line of greatest slope If and are their coefficients of friction with the plane and tana prove that if they are both on the point of slipping

Top of a wedge made of a very light material has two frictionless inclined planes A block of mass m is placed at the bottom of the inclined planes and another block of mass M is held motionless at the top of one of the inclined planes as shown in the figure Find range of values of m in terms of M and the angle of inclination so that when the upper block is released the lower block starts sliding up the wedge

A rocket with lift off mass of 10 metric ton is blasted upwards with an initial acceleration of 2 2 m s What is initial thrust of blast g 9 8 m s 105 kN 112 kN

A block of mass 30 kg is resting on a horizontal table 1 5 m from its edge The block A is attached to string whose other end is carrying a body B of mass 3 kg If the coefficient of friction between the block A and the table is 0 06 find the acceleration of the system and the time required to fall over the edge 30kg A 1 5m

A cricket ball of mass 250 g with a speed of 10 m s is hit back by a bat and returns with same speed within 0 01 s The force exerted by the bat is 200 N 400 N 500 N

A 5 A block of mass 1 kg placed on ground is pulled by a string by applying 10 N force g 10 m s 1 ii Draw F B D of block Give action reaction pair involved in the above problem 10 N 1kg earth

5 Two inclined rollers each of weight Q 2000 N are supported by an inclined plane and a vertical wall as shown below Assuming smooth surfaces find the reactions induced at the points A B and C 166 30 5

A ball of weight Q 120N rests in trough ABC as shown in fig A Determine the forces exerted on the sides on the vertical face D and on the inclined face at E if all the surfaces are perfectly smooth E C 12 11 20

Block B 15 kg is located on a frictionless horizontal table and attached to a hanging block C over a frictionless pulley as shown in Figure A2 Block A 8 kg is placed on top o block B The system is then released from rest Given the static coefficient of friction between blocks A and B us 0 65 Determine the maximum mass of block C such that block A will not slide on block B A B

Two blocks are kept on an inclined plane and each other with a mass less string Coefficient of friction between m and inclined plane is and between m and the inclined is 2 Then m 1 m2 1 tan 0

A plank P and block Q are arranged as shown on a smooth table top They are given velocities 3 m s and 6 m s respectively The length of plank is Im and block is of negligible size After some time when the block has reached the other end of plank it stops slipping on plank Find the coefficient of frictio between plank P and block Q if mass of plank is double of block 6 m s Q D 3 m s

3kg are connected to each other with light string and are then placed on a smooth frictionless surface The system is pulled with force F from side of the lighter mass so that it moves with an acceleration of 1ms 2 T and T denote the tension in the other strings The value of F is 1m s 2kg T 3kg T 5kg 2 42 7

Two blocks A and B of masses 2 kg and 4 kg respectively are interconnected by an ideal spring of constant 200 N m and placed on a smooth horizontal surface If the spring is initially unstretched and block B is given a rightward velocity 10 m s then the maximum extension attained in the spring will be 1 3 A 2 3 m 4 3 00000 10 m s B 21 1x 4x10 nd 20 n 2 2 m 4 1 89 m

QTwo bars 1 and 2 are placed on an inclined plane forming an angle a with the horizontal The masses of the bars are equal to m and m2 and the coefficients of friction between the inclined plane and these bars are equal to k and k respectively with k k2 Find the minimum value of a at which the bars start sliding down 1 2

Following are some gases with their compressibility factor values at S T P The gas supposed to deviate least from ideal nature is 1 Gas A Z 1 15 2 Gas B Z 0 98 4 Gas D Z 0 92 3 Gas C Z 0 86 ompressibility

QA uniform disc of mass m and radius R rolls without slipping up a rough inclined plane at an angle of 30 with the horizontal If the coefficient of static and kinetic friction are each equal to and the forces acting on the disc are gravity and contact force then find the direction and magnitude of the friction force acting on it

A person of mass M kg is standing on a lift If the lift moves vertically upwards according to given v t graph then find out the weight of man at the following instants g 10 m s i t 1 second ii t 8 seconds iii t 12 seconds s 20 2 8 B 10 12 14 t s

b 4 0 kg c 0 2 kg d 0 4 kg a 2 0 kg 17 Two masses m 5 kg and m 4 8 kg tied to a string are hanging over a light frictionless pulley What is the acceleration of the masses when lift is free to move take g 0 8 ms 2 b 9 8 ms 2 a 0 2 ms c 5 ms 2 d 4 8 ms 2 m m

a 0 2 ms c 5 ms 2 d 4 8 ms 2 18 In the given figure the pulley is assumed massless and frictionless If the friction force on the object of mass m is f then its acceleration in terms of the force F will be equal to a F f m c F 2m m b f m F 2 d None of these m

50 A small steel ball is dropped from a height of 2 5 m into a tall glycerin jar It hits the surface of glycerin with certain velocity and sinks to the bottom by losing 20 of its velocity at the surface If the time taken to reach the bottom after it is dropped is 2 s and velocity in glycerin is lost at constant rate then find the average velocity of the ball over the whole journey

A man of weight w is in an elevator of weight w The elevator accelerates vertically up at a rate a and at a certain instant has a speed V a What is the apparent weight of the man b The man climbs a vertical ladder within the elevator at a speed v relative to the elevator What is the man s rate of expenditure of energy power output

long helix made of thin wire is held vertical The radius and pitch of me helix are R and p respectively A bead begins to slide down the elix D i Find the normal force applied by the wire on the bead when the speed of the bead is v Eventually the bead coefficient of friction between the wire and the bead acquires a constant speed of vo Find the FOOD R

1 Homogeneous plate of a constant thickness is loaded by two forces Fi 8 kN and F2 6 kN The force Fi lies in a plane perpendicular to the upper plane of a plate the force F2 is vertical The plate is suspended by a joint at point 4 bars 1 2 and a rope 3 Determine the reactions in all supports if p 7850 kg m a 1m and a 45 al a 50 wwww 2a 2

28 A small mass slides down an inclined plane of inclination 0 with the horizontal The co efficient of friction is o x where x is the distance through which the mass slides down and o a constant Then the distance covered by the mass before it stops is 4 b tane Hoqqu 1 d tane Un 2 a tan 0 Ho 1 c tane 2110

conveyor 0 A man of mass 60 kg is standing 2 belt When the belt is given an acceleration of 1 ms the man remains stationary with respect to the moving belt If 2 g 10ms 2 the net force acting on the man is 0 8 a zero c 60 N F ma 60x1 60 m 2 a 1 m ms b 120 N d 600 N

Two solid spheres of different mass radii and density roll down a rough inclined plane under identical situation Their time to come down is independent of their Question Type Single Correct Type 1 Mass 2 Radius 3 Density

A thin rope AB has a total mass m length and has its mass per unit length varies linearly from zero at end A to some maximum value at end B It is kept as a heap on a horizontal surface The end A is pulled horizontally away from the heap by applying a force F on it At any instant the length of the rope pulled out is say x Assume that the heap as such is stationary there is no friction in the rope with itself Neglecting the weight of the pulled out rope Then Q7 What is the force F to have a constant velocity of the pulled out part

A 63 9 N diver stands at the edge of a 6 70 m diving board with a mass of 6 15 which is connected to two narrow pillars 2 00 m apart as shown Find the magnitude of the force exerted on the diving board by pillar A Round your answer to the nearest whole number 2 00 m B L

112 A car accelerates from rest at a constant rate of 2 m s for some time Then it retards at a constant rate of 4 m s and comes to rest If it remains in motion for 3 seconds then the maximum speed attained by the car is 1 2 m s 2 3 m s 3 4 m s 4 6 m s

2 A bullet leaves a rifle with a muzzle velocity of 521 m s While accelerating through the barrel of the rifle the bullet moves a distance of 0 840 m Determine the acceleration of the bullet assume a uniform acceleration

3 m B 5 m 4 m 6 A uniform right angled triangular lamina is suspended from the ceiling with the help of three light strings The plane of the lamina is horizontal and the strings are vertical as shown in the figure In which of the following options tensile forces TA TB and Tc developed in the strings connected to the vertices A B and C respectively of the lamina are arranged in correct order of their magnitudes C a TA TB TC b TB TA TO c TC TA TB d TA TB TC

5 To drag a block up an inclined plane with a constant speed a force F has to be applied along the line of fastest descent whereas to drag the block down the plane with a constant speed a force F has to be applied along the line of fastest descent as shown in the following figure Find the minimum horizontal force F parallel to the plane required to slide the block F F2

Q4 A 4 m bar of negligible weight rests in a horizontal position on the smooth planes shown in F Compute the distance x at which load T 10 kN should be placed from point B to keep the b horizontal 1m 30 P 20 KN 4 m T X 45 T

MathJax webview Use g 9 80 m s2 In the figure shown we have R 0 20 m m1 12 0 kg m2 18 0 kg and I 1 60 kg m2 Assuming there is no friction a Calculate the angular acceleration of the heavy roller of radius R and moment of inertia I b Calculate the linear acceleration of the masses c Calculate the voltage T1 rad s m s N a a b a c T1 m1 T Direcci n del Movimiento I T

above the floor It bounces back repeatedl 81 always rising to 100 of the height throug which it falls Find the average speed of the bal Take g 10 ms 2 1 3 0 ms 1 3 2 0 ms 1 Official Ans by NTA 4 l 4 Vo 2gh e 2gh 2gh t e 0 9 S h 2e h 2e4 h 2h 2e DD 2 3 50 ms 1 4 2 50 ms 2h 2e g 6 0 2h g

In the figure shown blocks A B and C are kept over each other and are placed on ground then A B C A net force on each block is zero B normal contact force between ground and block C is equal to the combined weight of all blocks C if an downward force is applied on block A normal contact force on each block will increase D Total two forces are acting on black C

A block of weight W is kept in equilibrium by two forces P and Q as shown in the figure Which of the following give the condition for the block to be in equilibrium A WP tane C W Q sine and P Q cose Q 0 W Vertically upward direction P Horizontal B WP cote D P Q sine and W Q cos

a An Electric Bulb weighing 180 Nis suspended between wall and the roof by the two wires as shown in figure Determine the tension in the wires using Lami s theorem 06 Marks C O No 4 Comprehension 45 60 b What is meant by equilibrium of a rigid body State the conditions of static equilibrium for coplanar non concurrent force system 04 Marks B

A uniform heavy rope of mass 8 kg and length 100 cm is being pulled as shown Choos CORRECT statement s 40 N A Acceleration of rope will be 5 m s B Tension in rope at 25 cm from it s left corner will be 10 N C Tension in rope at 75 cm from it s left corner will be 30 N D Tension in rope at 50 cm from it s left corner will be 20 N