Newton's law of motion Questions and Answers

13 Which of the following graphs represents the distance time variation of a body released from the top of a building 1 3 s t 2 S 4 s t cash Educational Services Limited Regd Office Aakash is different plz explain Sir Tom my point of view it should be pt 4 But given

26 A heavy rope of mass m and length on a smooth table It is pulled at both ends by applying force F of equal magnitude as shown Tension in the rope at point 1 1 A is 3F 4 2 B is F 2 3 A is F FR B A R E TRA an faci e 4 2

A particle of mass m 2 kg is placed on the top of a smooth hemisphere of mass M 4 kg The hemisphere is placed on smooth ground The particle is displaced gently Then ratio of magnitude of normal reaction and pseudo force seen from the hemisphere frame acting on the particle when angle 0 30 see figure Assume that the particle remains in contact with the hemisphere MI

Question No 3 Single Correct A A A stone is thrown with speed u from the top of a tower reaches the ground with a downward velocity 4u The height of tower 15u 2g 7u 2g 16u 9

Laws of Motion 99 A Due to inertia an object is unable to change by itself its state of rest and uniform motion R An object cannot change its state unless ed emal force

A block of mass M is pressed against a wall with a horizontal force F Then a it will slide down if the wall is smooth b frictional force may balance the weight if the wall is rough c Normal reaction is equal to weight of the block d Normal reaction is zero if the wall is smooth A a and b are correct Mark For Review Next Clear Response K

8 A force time graph for a linear motion is shown in Figure where the segments are rectangular The linear momentum gained between 0 and 6 seconds is Force N 1 2 Ns ON 17 2 Time s 6 2 zero Ns n AL X CC RCC RCC RCC RCC RCC RCC

A sphere of mass m is held between two smooth 3 inclined walls For sin 37 the wall 2 is equal to a c 16 mg 25 39 mg 21 wkw 379 37 5 the normal reaction of b N my s097 3m 25 mg 39 d None of these support fixed to

A bus is moving with a speed of 10 m s on a straight road A scooterist wishes to overtake the bus in 100 s If the bus is at a distance of 1 km from the scooterist with what speed should the scooterist chase the bus A 40 m s B 25 m s C 10 m s D 20 m s

NO 134 From the figure if the mass is at equilibrium then find T and T2 300 600 T 200N A 100N 100 3N B 200N 100 3N C 100 3NN 200N D 100 3N 100N

When same force is applied on n different bodies then accelerations produced in them are respectively 1 1 1 1 2 3 4 1 acceleration will be n 1 2 1 2 3 all in m s2 If all these bodies are joined together same force is applied then 2 4 2 n n 1 n n 1

3 a b d A chain has five rings The mass of each ring is 0 1 kg This chain is pulled upwards by a force F producing an acceleration of 2 50 m s in the chain Then the force of action reaction on the joint of second and third ring from the top is 1 0 25 N 2 1 23 N 3 3 69 N 4 6 15 N

acceleration of the body relative to non inertial frame 1 A person holding a rifle mass of person and rifle together is 100 kg stands on a smooth surface and fires 10 shots horizontally in 5 s Each bullet has a mass of 10 g with a muzzle velocity of 800 ms The final velocity acquired by the person and the average force exerted on the person are 1 1 6 ms 1 8 N 2 0 08 ms 16 N 3 0 8 ms 16 N 4 1 6 ms 1 16 N

A frictionless pulley of negligible weight is suspended from a spring balance as shown in fig Masses of 1kg and 5 kg are tied to the ends of string which passes over the pulley The masses move due to gravity The reading of the balance will be 1 more than 6 kg 2 6 kg 3 less than 3 kg 4 less than 6kg and more than 3kg 1kg 0000 5kg

1 1 a b 3 c d In fig speed of each particle after 4 sec 1 0 872 m s 3 0 218 m s 2 b c 4 a c 2 8 72 m s 4 2 18 m s Linear momentum of P of a body performing one dimensional motion is changing ere positive constants then net force acting ol T 11g B 11 5g

a 5 cms D 4 cm 1 A constant force acting on a body of mass 3 kg change its speed from 2 ms 1 to 3 5 ms in 25 s In the direction of the motion of the body What is the magnitude and direction of the force ka 18 m in the direction of motion b 0 32 m in the direction of motion c 0 64 m in the direction of motion d 0 16 m in the direciton of motion

Laws of Motion 91 8 An object of mass 2 kg at rest at origin starts moving under the action of a force F 31 1 4 N The velocity of the object at f 2 s will be

Board Competitive Exams 34 An object starts from rest and is acted upon by a variable force F as shown in figure If F is the initial value of the force then the position of the object where it again comes to rest will be A 1 2F tana 2 sina 38 A m TI 1 3 39 A pl fri H

m2 g Two masses are suspended vertically on a pulley their acceleration is mig m2 1 3 m m m m2 g Two blocks of mass m m 2 m 4 m m2 m2 m g C E

A person says that he measured acceleration of a particle non zero while any force is not actin on particle then 1 he is telling false 2 speed of his clock may be slow 3 His metre scale may be longer than standard scale LAY It may bo non inertial frame of reference

3 47 4 m s 4 37 47 m s 39 A block of mass m is at rest on a rough inclined plane of angle of inclination 0 If coefficient of friction between the block and the inclined plane is H then the minimum value of force along the plane required to move the block on the plane is 1 mglucose sino 3 mglucose sino 2 mg sine ucose 4 mg sino ucosi

A heavy rope is hanging between points A and B if mass of the rope is 90 kg A Tension at point A is 900 N B Tension at point B is 540 N C The horizontal component of tension force is different at each point of the rope D The vertical component of tension force is same at all the points of the rope 37 Y

3 30 kg 4 7 5 kg In fig a uniform rod of 3kg length 30 cm is shown String shown in figure are being pulled with constant forces of 20 N 30 N What will be the acceleration of rod 1 2 m s 3 4 m s A 20N 10cm 20cm 2 3m s 4 6 m s tring such mass of 18 kg remain stationary 32

0 A ball of mass 50 g is dropped from a height of 20 m A boy on the ground hits the ball vertically upwards with a bat with an average force of 200 N so that it attains a vertical height of 45 m The time for which the ball remains in contact with the bat is Take g 10 m s 1 1 20th of a second 2 1 40th of a second 3 1 80th of a second 4 1 120th of a second

Two small balls of the same size having masses m and m2 m m are tied by a thin weightless thread and dropped from a certain height Taking the force of buoyancy of air into account the tension T in the thread during the flight after the motion of the ball becomes uniform will be A m m2 g B m m 1 1 Correct Answer Your Answer m m g 9

ring of mass m 30g slides over a smooth vertical rod Attached to the ring is a light string passing ove smooth fixed pulley at a distance of 0 8 m from the rod At the other end of the string there is a mass 50 g The ring is held level with the pulley and then released see figure Determine the distance by whic e mass m moves down before coming to rest for the first time m

Two blocks of mass m each are connected by a massless string while block A is connected to point O by another massless string Both rotate with constant speed w on the horizontal surface with O as centre It T is the tension in OA and T is tension in string AB then the relation between T and T2 is m m r2 r A B

Question No 11 A 20 kg block attached to a spring of spring constant 5 N m is released from rest at A The spring at this instant is having an elongation of 1 m The block is allowed to move in smooth horizontal slot with the help of a constant force of 50 N in the rope as shown The velocity of the block as it reaches B is assume the rope to be light 50N O 4 m s 2 m s 0 1 m s O 3 m s ooooo OO TA A 4m B 3m Save N

to 1 2 6 A 14 C M becomes half B 2 2L A L Arrangement 11 A Ratio of fundamental frequency of standing wave in wire A in arrangement 1 to B to C is equal C M C 3 L 3L Arrangement 2 B If A vibrates in fundamental mode while B vibrates in 1st orvertone no beats can be heard in arrangement 1 C Time taken by wave pulse generated at bottom of wire B in arrangement 1 to reach ceiling is more than average of similar times for wire A and wire C in arrangement 2 And D If L length of rod and wire B is cut in arrangement 1 tension in wire A suddenly 12

Consider the following two statements a Force of friction is dependent on area of contact b Friction force may also act when there is no relative motion between the contact surfaces The correct statement is O a only O b only O a and b both Neither a or h

two cylinders p and q rest in a channel the cylinder p has diameter of 100m and weight 200N where as the cylinder q has diameter at 180mm and weig 500N if the bottom width of the box is 180mm with one side vertical and other inclined at 60 degree determine the pressure at all the four points in contact

A ring of mass m can slide on the vertical smooth rod Ring is connected by block with string as shown in figure Pulley is massless smooth and the system is released from rest Initial tension in string is T Mg OT Mg OT Mg OT Mg mg m Ring Rod a M

A plane mirror is moving with velocity 42 5j 8k A point object in front of the mirror moves with a velocity 31 43 5k here is along the normal to the plane mirror and facing towards the object The velocity of the image is Only one correct answer A 32 4j 5k B 72 93 11k C 3i 43 11k D 3 43 11k

In the arrangement shown in the figure the mass of block B and A are 2m and 8m respectively The surfaces between B and floor is smooth The block B connected to block C by means of an ideal pulley If the whole system is released then the minimum value if mass of the block C so that the block A remains stationary with respect to B is coefficient of friction between A and B is A m 2m 4

9 Board Competitive Exams Two strings of same material are stretched to the same tension If their radii are in the ratio 1 2 then respective wave velocities in them will be in ratio 1 4 1 2 2 1

A particle is projected from ground from point A near the bottom of a wedge At the same time wedge sufficiently long is also moved with same speed towards right as shown then 8 10m s 10 3m s 30 10 3m s 60 A Particle can never collide the wedge B Particle will collide the wedge after 2 sec C Maximum height attained by the particle is 11 25 m from the ground D Height of point on the wedge where particle strikes is 10m

A uniform solid cylinder of mass m radius R is placed on a rough horizonta table A string attached to it passes over a pulley disc of mass m radius R that is mounted on a smooth axle A block is suspended at the free end of strin Cylinder rolls without slipping there is no friction between pulley and string System is released from rest Find out the correct option among the following m A Acceleration of the block will be g 3 2g B Acceleration of the block will be 5 mg C Friction on the cylinder will be 5 8 D Angular acceleration of pulley will 3R m

A heavy block of mass m is supported by a string C from the ceiling as shown in the figure Another string D is attached to its bottom If D is given a sudden jerk then 1 string C will break 2 string D will break

A railway carriage is moving on a horizontal track with an acceleration a A passenger sitting in the carriage drops a stone The acceleration of the stone relative to rail track will be 1 a 3 a g 2 2 g 4 zero

As shown in figure two forces are acting on a body If its mass is 5kg the value of acceleration generated is 1 2 m sec 3 1 m sec 2 3 m sec 4 4 m sec 4N 90 3N

three forces be applied on the particle A retarding force to stop a train has a specific magnitude If the speed of the train is doubled ho far will this retarding force stop the train at 1 equal distance 3 8 times the earlier distance 2 4 times the earlier distance 4 a twice the earlier distance

6 velocity m s velocity of 30 km h on the rough road The velocity time graph of a car is given B 25 20 15 10 5 C D 5 6 7 8 9 10 11 Time sec i If the car weighs 1000 kg What is the distance travelled by the car in first 2 s 012 3 4 ii What is the braking force applied at the end of 9 s to bring the car to stop in 2 s

A block of mass M is pulled with a rope on a frictionless surface If a force P is applied at the free end of the rope the force exerted by the rope on the block will be mass of rope is m Pm M m P 3 M m In a U tubo th PM M m P 4 MM m 2

3 increased 4 Nothing can be said Under the action of external forces a particle can remain stationary when 1 a constant force is applied to the particle 2 a variable force is applied on the particl 3 at least three forces be applied on the particle 4 The vector sum of the applied force is ze rotordin fin magnituda If the speed of the train is doubled ho

A block of mass 4 kg is suspended through two light spring balances A and I in parallel Then A and B will read respectively 1 4 kg and zero kg 2 zero kg and 4 kg 3 4 kg and 4 kg 4 2 kg and 2 kg

A thread is passing through a hole at the centre of a frictionless table At the upper end a block of mass 0 5 kg is tied and a block of mass 16 kg is tied at the lower end which freely hanging The smaller mass is rotated on the table with a constant angular velocity about the axis passing through the hole so as to balance the heavier mass The mass of the hanging block is changed from K so that it balances the hanging mass 16 kg to 1 kg without changing radius of circle in which 0 5 kg block is moving the fractional change in the angular velocity of the smaller mass is 8 again Find the value of K

is moving in right direction with a uniform velocity v and end of rod which is in contact with ground is moving in left direction with a velocity v Find the rate at which the angle is changing in terms of v v R and 0 Solution R Figure 1 52 x R cosece Differentiating with respect to time we get dx dt 11 Here x is the separation between centre of hemisphere and the end of rod Rate of change of x can be taken as the relative velocity of end of rod and hemisphere centre i e v v We are required to find the rate of change of 0 and rate of change of x we know so we have to develop a relation between x and 0 which is given as V2 R cosece cote iii An morning sun in h an angle the spe ground v cosa de dt iv Fi m han end of horizo speed the m string horiz u co v heig spee 4 0 vi

If the distance between earth and sun is increased by 2 then find percentage change gravitational force acting between them Hint Use Newton s universal law of gravitation

Two identical light springs of spring constant k and two balls of same mass m are threaded on a smooth rod and rotated slowly abou the vertical z axis as shown In the steady state the angular velocity of the system is w and the length of the springs increase to and 12 as shown Take k 1000 N m l 20cm l2 16 cm w 20 rad s the natural length of each of the springs is 1 1 x to cm Find the value of lo Z k k mmmm l m

A cubical block of mass m is released from rest at a height h on a frictionless surface of a movable wedge of mass M which is in turn is placed on a horizontal frictionless surface as shown in the figure Find the velocity of the triangular block when the smaller block reaches the bottom h M m a