Newton's law of motion Questions and Answers

In given diagram pulley and string are ideal block A of mass 2m and B of mass m are released from rest then B A 2m 2g A Magnitude of acceleration of A with respect to B is 3 B Displacement of A B will be equal C Distance covered by A B in 3s will be 15 m D Velocity of A and B are equal

Assuming frictionless contacts determine the magnitude of external horizontal force P applied at the lower end for equilibrium of the rod as shown in figure The rod is uniform and it s mass is m Wall 1 ta mg 2 2 3 tan 0 mg 2 sin 0 mg 2 cot 0 P

A radius vector of point A relative to the origin varies with time t as r at bt2 where a and b are constant The equation of point s trajectory is b 2 x 1 y a 2b 3 y 2 b 2 2 y a 2b 4 y x 2 a 2

A bullet of mass 40 g moving with a speed of 90 m s enters a heavy wooden block and is stopped after a distance of 60 cm The average resistive force exerted by the block on the bullet is 1 180 N 2 220 N 3 270 N 4 320 N

A 60 kg high jumper lands on a mat after her jump The mat brings her to stop after 1 0 seconds She was traveling at 5 0 m s when she landed on the mat Calculate the force in which the mat stops her

Two blocks of mass 2 kg and 4 kg kept on smoot horizontal surface and connected by a light rop are being pulled by 13 N and 24 N force a shown in the figure The tension force in the strim connecting the block is az 13 N 2 kg Smooth 1 4 N 2 11 N 4 kg 24 N 2 17 5 N Zero 24 30

OI M Initially stationary gets off of the boat by leaping to the left in an exactly horizontal direction Immediately after the leap the boat of mass M is observed to be moving to the right at speed v Mark the incorrect statement Neglect friction offered by water on boat Work done by man on boat is Mv M 2m Total work done on man is Velocity of centre of mass of system is zero O Work done by man on himself M 2 m

7 A reference frame attached to the earth a is an inertial frame by definition b cannot be an inertial frame because the earth is revolving round the sun 1986 2M c is an inertial frame because Newton s laws are applicable in this frame d cannot be an inertial frame because the earth is rotating about its own axis

A ball of mass m and a block of mass m are attached by a lightweight cord that passes over a frictionless pulley of negligible mass as in Figure The block lies on a frictionless incline of angle O Find the magnitude of the acceleration of the two objects and the tension in the cord My

Two blocks of mass m and 2m are connected with a spring of spring constant K and are kept on horizontal frictionless surface If we impart a velocity v to block of mass m towards right The velocity of centre of mass is 2m I3 V 3K 2 mmm mooooo m

Que 1 A body of mass m 10 2 kg is moving in a medium and experiences a frictional force F k v 2 Its initial speed is v 10 m s If after 10 s its energy is 1 4 times the initial kinetic energy the value of k will be 10 1 Kg ms 10 4 Kg s 10 3 Kg s 10 4 Kg m

The range of a projectile launched from ground is R on the surface of the earth For the same initial velocity and angle of projection on a planet where g is one fourth of that on earth the range will be R B 4R A C 16 D 16 R

A body resting on a rough horizontal plane requires a pull a force of 90 N inclined at 30 to the plane just to move it It was also found that a push of 110 N inclined at 30 to the plane just moved the body Determine the weight of the body and the coefficient of friction

2 53 A chain of 5 links each of mass 0 1 kg is lifted vertically with a constant acceleration 1 2 m s2 The force of interaction between the top link and the one immediately below it is a 5 5 N b 4 4 N c 3 04 N d 7 6 N

21 Ten one rupee coins are put on top of each other on a table Each coin has a mass m The reaction of the 6th coin counted from the bottom on the 7th coin is d 3mg f a 4mg b 6mg c 7mg 6

3 A small block is sliding on a frictionless inclined plane that is moving upward with a constant acceleration If the block remains at a level height what is the acceleration of the inclined plane Acceleration due to gravity is g a gtan b g cot 0 gtan 0 c g sin 0 4 In the arrangement shown the springs are light and have stiffness k Horizontal

18 A bubble is at the bottom of the lake of depth h As the bubble comes to sea level its radius increases three times If atmospheric pressure is equal to 1 metres of water column then

3 6 A spherical ball of mass m 5 kg rests between two planes which make angles of 30 and 45 respectively with the horizontal The system is in equilibrium Find the normal forces exerted on the ball by each of the planes The planes are smooth Section C Calculation of Tension 450 30 30

equal specific heat A steel ball of mass m 1 kg moving with velocity 50 m s collides with another ball of m2 200 gm lying on the ground During the elastic collision their internal energies ch equally and T and T are the rise in temperatures of masses m and m2 respectively If sp heat of steel is 0 105 and J 4 18 J cal then A T 7 1 C and T 1 47 C C T 3 4 K and T 17 0 K B T 1 47 C and T 7 1 C D T 7 1K and T 1 4 K

A stone of mass 0 05 kg is thrown in vertically upward direction with a speed of 20 m s Take g 10 m s If this stone experiences an air friction of 0 1 N the net force acting on the stone during upward motion A 0 4 N upward C 0 6 N downward B 0 4 N downward D 0 6 N upward

A 10 kg stone is suspended with a rope of breaking strength 30 kg wt The minimum time in which the stone can be raised through a height 10 m starting from rest is Taking g 20 Nkg A B C 0 5 s 1 0 s Correct Answer w 1 S

The acceleration of man of mass 40 kg plus block of 10 kg system shown in figure if the man applies a force 300 N on the string the plane in fixed smooth and horizontal also assume that the string is horizontal A 0 6 m s B Zero C 12 m s Correct Answer block man

In the figure shown k 200N m k k 400N m m 2kg and F 80N The system is at rest and in static equilibrium g 10 m s AX 90 K Now the force F is removed suddenly Then displacement of the block from the given instant to its equilibrium position is B 60m mumu 40am D 50pm

28 A car starts from rest and moves with uniform acceleration a on a straight road from time t 0 to t T After that a constant deceleration brings it to rest In this process the average speed of the car is a 4 b e 3a7 2 d ar

B 4 A cylinder of weight w is resting on a fixed V groove as shown in figure a Draw its free body diagram b Calculate normal reactions between the cylinder and two inclined walls 60 60 Smooth fixed

A half section of pipe of mass m and radius r rests on a rough horizontal surface Now a vertical force F is applied as shown Assuming that the section rolls without sliding the OB D Instantaneously for rolling without slipping the minimum co efficient of friction F 2 mg F between the surface should be

A Ferris wheel rotates at an angular velocity of 0 18 rad s Starting from rest it reaches its operating speed with an average angular acceleration of 0 035 rad s2 How long does it take the wheel to come up to operating speed

A cube of mass M 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 K 0 1 R L M Uz my Uk 8GR VAR K agR 1 3 mg 2 mg 2 2 N R R x mg 2x mg N mw

0 If two identical spheres having charge 16 C and 8 C are kept at certain distance apart then the force is F They are touched and again kept at the same distance the force becomes 24 2x 2 1 F 3 8 2 4 F 18 FN 2 24 32 2 24 3 kuom

Q 3 This is a calculus problem A stubborn mule of mass m sits down and refuses to move To drag the mule to the barn the exasperated farmer ties a rope around the mule and tries to pull the mule The coefficients of friction between the mule and the ground are 0 7 and 0 5 a Derive an expression for the angle at which the farmer should pull the mule in order that the applied force will be minimum b If the mass of the mule is 78 0 kg calculate the minimum force needed to make the mule just start sliding c Once the mule starts moving what minimum force is needed to keep this mule moving with constant speed

Paragraph for 19 to 20 Three planks 1 2 and 3 are arranged on a pulley system in a vertical plane as shown in figure Plank 1 has a mass of m plank 2 and plank 3 are massless All the pulleys are mass less and frictionless An external vertical force mg is applied over plank 1 Assume planks are very close to each other and they don t rotate wwwwwwwww 3 A mg T mg m If the whole assembly is taken in an elevator which is moving upwards with an acceleration g the reaction between plank 2 and 3 will be B 2 mg ww www we C mg The reaction between 2 and 3 if the elevator falls freely A mg B mg 3 C mg 2 D zero D zero

For the system shown in figure all the pulleys are light and frictionless and strings are deal Initially the system is held at rest by some external means Now the system is released i e external effect has been removed but still it has been observed that 10 kg and 5 kg blocks are not moving This is possible when for 5 and m are both equal to kg 2 A m B sum of m and m is 5 kg C many possible values of m and m 5 D harmonic mean of m and m is kg 2 10kg 5kg m

In the arrangement shown in the figure a wedge of mass m 3 45 kg is placed on a smooth horizontal surface Small and light pulley is connected on its top edge as shown A light flexible thread passes over the pulley Two blocks having mass m 1 3 kg and m 1 5 kg are connected at the ends of the thread 171 m m 37 m is on smooth horizontal surface and m rests on inclined smooth surface of the wedge The base length of wedge is 2 m and inclination is 37 m is initially near the top edge of the wedge If the whole system is released from rest calculate a Velocity of wedge when m reaches its bottom b Velocity of m at that instant g 10 ms 2

20 A particle is projected with velocity 20 ms at angle 60 with horizontal The radius of curvature of trajectory at the instant when velocity of projectile becomes perpendicular to velocity of projection is g 10 ms 1 60 3m 21 A uniform I chonad 80 2 m 3 80 3 3 in the four The englo 4 cuch that 3 40 3m m

21 In the given figure the rough hofizontal surface has a frictionless vertical groove A massless bar can move freely into the vertical groove It is attached to a spring of force constant k Now two solid spheres each of mass M are rotated to high angular velocity and placed in the corners as shown The co efficient of kinetic friction between the spheres and the bar and between the spheres and the horizontal surface isu Then the compression of the spring is 2 Mg A B C D 1 p Mg Mg 1 k Mg k M 0 000000 0 M

Pre Medical Physics 167 batsman deflects a ball by an angle of 90 without changing its initial speed which is equal to 54 km hr What is the impulse imparted to the ball Mass of the ball is 0 15 kg sool C The magnit

hangs from a point C and BC The string AC is in the horizontal and BC at 45 horizontal assal shown in Fig Using Lami s theorem or otherwise determine the forces in the strings AC 2 Points 10 5 N 11 N 11 5 N 10 N B 45 C trings AC 15 N to 60 A

One equilateral wedge and two other wedges are arranged on a rough horizontal surface as shown in the figure Now wedge 1 and 3 are moved horizontally with the velocity 10 3 cm s as shown If velocity o the wedge 2 is x cm s Find the value of x 1043 cm s 2 10 3 cm s

The force between two identical particles separated by distance d is F Four such identical particles are placed at the corners of a square of side d The magnitude of net force on any particle will be 2 2 1 F Zero 2 2 1 5 2 2 2 1 2 2

A spring of unstretched length has a mass m with one end fixed to a rigid support Assuming spring to be made of a uniform wire the kinetic energy possessed by it if its free end is pulled with uniform velocity v is WRITE VELOCITY INTERMS OF VARIABLE 2 mv 4 mv 1 1 mv 2 1 3 mv 3 question meaning not Linderstood 2014

Three blocks are kept as shown in figure of 20 kg block with respect to Acceleration ground is 10 kg 20 kg 30 kg 1 5ms2 2 2 ms 100 N 0 5 0 25 0 3 1 ms 4 0

A collar can slide on a semicircular rod of radius 1 m in a vertical plane The collar has a weight of 25 N and the attached spring has an unstretched length of 1 m The other end of spring is fixed to point A At the instant 0 30 the collar is released from rest Neglect friction k 30 N m mm A The normal force on the collar is 1 m

a Band Example 2 17 Resolve a weight of 10 N in two directio are parallel and perpendicular to a slope inclined at 30 to the horizontal Sol Component perpendicular to the plane 30 WI 30 W W 10 N

A block of mass m 4kg is placed over a rough inclined plane having coefficient of friction 0 6 as shown in fig A force F 10N is applied on the block at an angle 30 The contact force between the block and the plane is 309

ajo kg what will be observed weight of the person as recorded by the balance when elevator ca moving downward with a velocity of 20 m s is being stopped and in the process a deceleration 2 is acting on it VR 180301 ZAMO a 70 kg c 50 kg b 90 kg in ka

32 A body of mass m rests on a horizontal floor The coefficient of static friction between floor and body is u The minimum possible force that has to be applied to make the body move is 1 mg AST mg 2 1 2 1 mg mg 4 2 VM 1

Q 6 In the figure the blocks are of equal mass The pulley is fixed In the position shown A moves down with a speed u VB the speed of B BA Answer B will never lose contact with the ground mm The downward acceleration of A is equal in magnitude to the horizontal acceleration of B UB ucose Rate this

U Two blocks A and B are pushed against the wall with the force F as shown in the figure The wall is smooth but surfaces of A and B in contact with each other are rough Which of the following is true for the system of blocks to be at rest against the wall F BA 4 wall 1 F should be equal to the weight of A and B 2 F should be more than the weight of A and B 3 F should be three time the weight of A and B 4 System cannot be in equilibrium

QTwo blocks are in contact on a frictionless table A horizontal force is applied to one block as shown figure If m 10kg and m2 5kg and F 15N Find the force of contact between the two bodies A C F B F 3N D F 5N F 4N F 2N m1 m

6 What should be the value of angle O so that motion of the block 200N impends down the plane in Fig 1 take 0 3 for all contact surface 100N 200N e Fig 1 String E W A 60 100N D Fig 2 B 6000N 40 F