Newton's law of motion Questions and Answers

A block of mass 5 Kg starts moving on smooth x y plane under an unknown force only If area of Fx v s time curve is 4 N s and area of Fy v s time curve is 2 N s for a given time interval Then work done in J by the unknown force will be

A particle is projected vertically upwards from a point A on the ground It takes t time to reach a point B but it still continues to move up If it takes further t time to reach the ground from point B then height of point B from the ground is A g t t C g t t B gt t D gt t

Example 6 The blocks are attached by an inextensible light string and pulled vertically upward by force 100 N as shown Find the common acceleration and tension in the ering using luter lang thange equation 100 2 kg 3 kal

3 An insect crawls up a rough hemispherical bo with coefficient of friction 0 5 If the line joining the centre of hemispherical bowl with the inse makes angle 0 with the vertical then maximu value of 0 is 1 tan 2 3 sin 0 5 SS A 2 cos 0 5 4 dot 1 2

and 2 38 A fixed pulley carries a weightless thread with masses m m at its ends There is friction between the thread and the pulley It is such that the thread starts slipping when the ratio m m no find a The friction coefficient b The acceleration of the mass when m m no Ans In no a T m no g n no

passes through the centre is cut What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre 1 15 MR 32 3 11 MR 32 2 13 MR 32 4 9 MR 32 anah gerare for a w en fr free he f muft or 1 15 MR 32 3 11 MR 32 simp 2

Two balls of mass M and 2M are thrown horizontally with the same initial velocity vo from top of a tall tower and ex perience a drag force of kv k 0 where v is the instanta neous velocity Then WHICH BALL FALLS FIRST light or heavy one WHY expla in Two balls of mass M and 2M are thrown horizontally with the same initial velocity vo from top of a tall tower and experience a drag force of kv k 0 where v is the instantaneous velocity Then vo

Pulley of atwood machine has mass m and is free to rotate about its geometrical center without friction Centre of mass of the pulley is at a distance R 2 from geometrical centre where R is the radius of the pulley There is no slipping between the string and pulley The ratio of maximum acceleration to minimum acceleration of block of mass m is Take m R as moment of inertia of pulley about axis of rotation m m 3 m m m m

6 30 A system consists of a thin ring of radius R and a very long uniform wire oriented along axis of the ring with one of its ends coinciding with the centre of the ring If mass of ring be M and mass of wire be per unit length calculate interaction force between the ring and the wire ci

u 0 2 guns situated on the top of a high hill fire a shot each at some interval o time with the same speed 5 3 m s One gun fires horizontally and other fi upwards at an angle of 600 with the horizontal The shots collide in air at point P g 10 u I The time interval between the firing II The coordinates of P taking top of the hill as the origin P x y un

A bock of mass 5 kg is placed on a smooth table an tied from both ends by two masses 3 kg and 2 kg b means of light inextensible strings passing throug pulleys as shown in the string connecting 5 kg and 3 kg is is g 10 m s A 22N B 27 N C 33 N D 30 N Q 3 kg 5 kg 3 kg

ixed at point motion of the at origin is very small engths are at a certain the field on the sign 9 3 3 cm 4 2 cm What is the force on a dip le of dipole moment P placed as shown in figure P O q a qP 1 4 a qP 3 2 a q 2 Zero qp Tena 4 10 A smooth tunnel is made in a sphere of radius R along its diameter The uniform volume charge Ephere particle of mass m and the sphere

0 50 A pendulum of length is given a horizontal velocity at the lowest point of vertical circular path as shown In the subsequent motion the string gets slag at a certain point and the pendulum bob strikes the point of suspension If the value of tan 0 N then the value of N is 0 is angle made by string with vertical at slag point as shown l slag

Question 30 For a ladder resting against a wall and floor having a weight of W N the direction of friction offered by the wall will be towards the wall away from the wall towards the floor away from the floor

A 25 kgf weight P is held in equilibrium by two st rings which run over two pulleys Counterbalanc es Q and R are attached to free ends of the string s One of the counterbalances weighs 20 kgf the sine of the angle formed by the string and the ver tical is 0 6 Neglecting friction of the pulleys dete rmine the weight R of the other counterbalance and the angle a formed by the second string with the vertical The weight of the strings may be neg lected a B RP A 20 kg 53 B 20 kg 37 C 15 kg 37 D 15 kg 53

The following figure shows a painter in a swing suspended along a building When the painter pulls the rope the force exerted on the floor is 450 N while the weight of the painter is 1000 N If the weight of the swing is 250 N the value of acceleration produced in the swing will be a 4 m see b 2 m sec e 5 m sec d 6 m sec

pr 12 A rope with mass m is hung from the ceiling by its both ends and a weight with mass M is attached to its centre The tangent to the rope at its either end forms angle a with the ceiling What is the angle 3 between the tangents to the rope at the weight a B M m

A uniform elastic rod of cross sectional are A natural length L and young s modulus Y is placed on a smooth horizontal surface Now two horizontal force of magnitude F and 3F direction along the length of rod and in opposite direction act at two of its ends shown After the rod has acquired steady state the extension of the rod will be Elastic rod 3F

2 A circular disc rotates at 60 revolu is placed at a distance of 8 cm from the centre of the 3 What is the acceleration of the block and the trolley system shown ion fig if the coefficient of friction between the trolley and the surface is 0 04 Also calculate the tension in the string 10kg I 2kg nd 16 98 N

The benches of a gallery in a cricket stadium are 1 m wide and 1 m high A batsman strikes the ball at a level one metre above the ground and hits a mammoth sixer The ball starts at 35 m s at an angle of 53 with the horizontal The benches are perpendicular to the plane of motion and the first bench is 110 m from the batsman On which bench will the ball hit

97 A solid sphere of radius r is resting on a smooth horizontal surface A constant force F is applied at a height h from the bottom Choose the correct alertnative F TO ANO The dri ALLEN 1 Sphere will always slide whatever be the value of h 2 Sphere will roll without slipping when h 1 4r 3 Sphere will roll without slipping if h 1 4r 4 Sphere will roll without slipping if h 1 4r 97 To tho vo 34 OL

A ball of mass 250 gm collides on the wall of billiards table with 2 m s After remaining in contact with the surface for 0 02 s it rebounds with 1 8 m s Calculate approximately the magnitude of average force exerted on ball by the surface 1 40 N 2 48 N 3 25 N 4 None

Consider two particles P Q such that P moves under the action of force F mg And Q moves under the action of force F mg If both the particles are projected from same point with same speed at same time at an angle 8 with horizontal then distance between both the particles 2 sec after the projection will be g constant 10m s 18 G

Particle a starts from rest at t 0 from x 0 with constant acceleration to reach x 1m at t 1 s Also at t 0 particle b starts with uniform velocity from x distance covered by particle b in the frame of reference attached to particle a from t 0 to t 1 Im to reach x 2m in 1s The is 1 k meter Then find the value of k

18 A block of mass m is placed on an inclined plane with angle of inclination 0 Let N f and F respectively represent the normal reaction limiting force of friction and the net force down the inclined plane Let u be the coefficient of friction The dependence of N f and F on 0 is indicated by plotting graphs as shown below Then curves 1 2 and 3 respectively represent A N F and fl B f F and N 3 2 1 2 C F N and fr D fL N and F

Q 20 A small box of mass m is placed on top of a larger box of mass 2m as shown in the diagram at right When a force F is applied to the large box both boxes accelerate to the right with the same acceleration If the coefficient of friction between all surfaces is u what would be the force accelerating the smaller mass F A mgu B F 3 mgu m 2 m F C F mgu D F mgu 3

A balloon with mass m is descending acceleration a where a g How much mass should be removed from it so that it starts moving up with an acceleration a Assume that it s volum does not change m Fa ma Fax m am g 4m 2 ma 3 2 2ma g a 2 2ma g a ma g a an 4 g a

and B if the pulley and the table are perfectly smooth the acceleration of the 5 kg body in case A and B are 4kg B A gand 5 9 g B 4 9 g and 1 9 g C g 5 and g 5 D 5 9 g and 1 9 g 5kg 5kg A 4kg

shown in the The two pulley arrangements figure are identical The mass of the rope is negligible In a the mass m is lifted up by attaching a mass 2m to the other end of the rope In b m is lifted up by pulling the order end of the rope with a constant downward force of 2mg The ratio of acceleration in two cases will be a m 2m m 2mg

26 PHYSICS If acceleration of block B w r t A is 2m s2 just after the system is released from rest then mass in kg of block C will be pulley and string both are massless take g 10 m s BA 0B QA 2 AB 89 5kg N 0 6 A P 0 2 5kg B 10 85 0 6X 50 570 QAZ6

Asystem of two blocks is placed on an accelerating conveyor belt If there is no slipping between 6 kg block and conveyor belt and friction coefficient between 4 kg 6 kg block is 0 5 then frictional force acting between 6 kg conveyor belt will be Poggio 18 OT 4kg u 0 5 6kg 8m s

Q 22 With what minimum velocity should block be projected from left end A towards end B such that it reaches the other end B of conveyer belt moving with constant velocity v Friction coefficient between block and belt is A ugL B 2 gL Am Ve VE L B C 3 gL D 2 gL

Q 6 A triangular prism of mass m with a block of mass m in placed on it is released from rest on a smooth inclined plane of inclination 0 The block does not slip on the prism Then rough m mi smooth fixed A the acceleration of the prism is gcose B the acceleration of the prism is gtane C the minimum coefficient of friction between the block and prism is min cote D the minimum coefficient of friction between block and prism is min tane

8 The co efficient of friction both static and kinetic between the inclined plane and the block A of mass 1 kg is 1 3 whereas there is no friction between block B 1 kg and the inclined plane The system starts from rest When the system covers a distance s 30 m on the inclined plane the cord between Aand B is burnt off The velocity of A when it covers a further distance of 20 m on the inclined plane is A Zero B 120m s B 30 A C 150m s D 300m s

A wedge and a block system is released from rest in the given arrangement If all surfaces are smooth and acceleration of wedge with respect to ground is 2 m s towards left then choose INCORRECT option IMF A Magnitude of acceleration of block with respect to ground is different from its acceleration magnitude with respect to wedge B Magnitude of acceleration of block is same with respect to ground and with respect to wedge C Magnitude of acceleration of block is 2 m s with respect to wedge D Magnitude of acceleration of block is 2 m s with respect to ground

A system consists of three masses m m and m3 connected by a string passing over a pulley P The mass my hangs freely me and m3 are on a rough horizontal table the coefficient of friction p The pulley is frictionless and is of negligible mass The downward acceleration of mass m is Assume m m m3 m 1 m g 1 2 9 g 1 2 m eq 3 m3 mog m m ug mit M2 Ms 2 4 2g 3 g 1 2

A box of mass 4 8 kg is being pushed against a wall by a force Fapp acting at an angle of 29 above the horizontal The coefficient of static friction between the box and the wall is 0 38 and the coefficient of kinetic friction is 0 30 a What is the minimum value of Fapp needed to keep the box from slipping downward b Suppose the value of Fapp is reduced to one half this value Find the acceleration of the box Fore 29

A 1200 kg car traveling initially at vci 525 0 m s in an easterly direction crashes into the back of a 9000 kg truck moving in the same direction at VT5 20 0 m s Fig P9 22 The velocity of the car immediately after the collision is vcf518 0 m s to the east What is the velocity of the truck immediately after the collision Ach VTJ

be 184 In the figure shown string Bis hat of 6 m s then find upward speed of block C is 37 O 1 1 5 m s m C 13 B 6 m s 2 3 m s

kowns related to that force Which shows a complete set of unknown quantities Why A F Fy F B a p Y C F a p D all of the above E both options A and C n 3 D when you don t know the direction or the magnitude of a force there are three un kowns related to that force Which shows a Vall

Two blocks of same mass m are released from the position as shown in the figure All surfaces are smooth Find the magnitude of normal force with which block B presses on the wall and accelerations of blocks 37 A B

19 Forces exerted by a uniform electric field on an electron having mass m and proton of mass m are represented as F and F respectively are related as a F F c 4 1 F p b d F F F F 11 m m 20 m 2 m

267 Two blocks A and B of masse connected by a string The block of mass 4n connected by a spring massless The string is suddenly cut The ratio of magnitude of accelerations of masses 2m and 4m at that instant are 1 1 2 px 00000 JONS 4m B 2m A pwon introshor 2 X 1xM m 08 3 1 4 bla fuorifiw MOS S MAS 2 M 8 A O A AS moins

In the arrangement shown 1 kg block rests on a 1 kg bracket All the surfaces are smooth Choose the correct options zef a ga 1 kg 1 kg fagmazm 92 71 ah qaz f fac CHRI 25 N A B C 10 ms 1 kg Acceleration of the bracket is 5 ms 2 R 5 ms Correct Answer 10 N 2 Acceleration of the bracket is 7 5 ms 7 5 ms 2 2 1 kg D 2 5 ms Acceleration of the block w r t bracket is 2 10 ms 2 Acceleration of the block w r t bracket is 2 de ce ar 5 ms 2

82 180 Consider string spring balance and pulley to massless g 10 m s2 in the given figure What is the reading of spring balance 2 m s 1 16 N 2 32 N 3 26 6 N 4 201 AT 1 kg Fig 2 kg

A man of 60 kg weight is standing at rest on a platform He jumps up vertically a distance of 1 m and the platform at the same instant moves horizontally forward with the result that the man lands 1 meter behind the point on the platfrom from where the took the jump the total work done by the man at the instant he lands is a 300 J b 150 J c 600 J d zero

t for vertical firing If then how much gas rocket an upward 10 m s 18mm 1 low nless surface with leak occurs in the te of 4 kg s What 250 s if the mass 3 2 5 m s 185 A ball is held in position A by The horizontal string is cut The tension in string OA just after the horizontal string cut is mg cose 3 mg sine 90 0190 100 king 2 mg cose 4 mg sin e

252 In the given figure all the surfaces are smo wedge starts moving with an acceleration a g cot then time taken by the block to reach the bottom of the wedge is rebr ingades 2h Vgcote 60 estan G 0 g solt A BAS

65 A mass of 1 kg is put on a pan and spring is stretched from its equilibrium position by 10 cm When pan is released the block just gets detached for a moment What should be the minimum value of spring constant for which this can happen Take g 10 ms 2 1 10 N m 2 100 N m 3 1000 N m 4 1 N m 00000000e mam

16 Two masses as shown in the figure are suspended from a smooth massless pulley The acceleration of 3 kg mass when system is released will be NCERT I XI Pg 106 LLLL 1 11 1 2 5 m s 2 kg 3 kg 2 2 0 m s LAX F 0 min