Newton's law of motion Questions and Answers

3 A ball of mass 0 1 kg is suspended by a string It is displaced through an angle of 60 and left When the ball passes through the mean position the tension in the string is a 19 6 N c 9 8 N 9 8 N 9 8 b 1 96 N d Zero IX my

2 23 Two blocks A and B of mass 1 kg and 2 kg respectively are connected by a string passing over a light frictionless pulley Both the blocks are resting on a horizontal floor and the pulley is held such that string remains just taut At the moment t 0 a force F 201 N starts acting on the pulley along vertically upward direction as shown in figure 2 206 Calculate a Velocities of A when B loses contact with the floor b Height raised by the pulley upto that instant F A B

An aircraft is moving with velocity of 300 ms If all the forces acting on it are balanced then a It will move with constant speed b It will move with constant velocity c It will fall down instantaneously d It will lose its velocity gradually

Two astronauts A and B connected with a rope stay stationary in free space relative to their spaceship Mass of A is more than that of B and the rope is straight Astronaut A starts pulling the rope but astronaut B does not If you were the third astronaut in the spaceship what do you observe A Astronaut B accelerates towards A and A remains stationery B Both accelerate towards each other with equal accelerations of equal modulus C Both accelerate towards each other but acceleration of B is greater than that of A D Both accelerate towards each other but acceleration of B is smaller than that of A

3 Figure shows x t y t diagram of a particle moving in 2 dimensions If the particle has a mass of 500 g the force acting on the particle is XA m 2 1 0 1 2 3 a t s a 1 N along y axis c 0 5 N along x axis y m 4 3 2 1 1 1 123 t s b b 1 N along x axis d 0 5 N along y axis

A man of mass m is inside a box of same mass The whole system is suspended with ideal strings and pulleys as shown in the figure The tension T in the string so as to keep the system in equilibrium is LLLLL LLLLLL ineribent to 1006 1320n 1 0975 1 mg es am mg d 3 T levi mstaveni no sono T by ed yel L inmatricar old to viooley is vticoley isdimg s bold orl of 4 A 2 m 2 2 mg mp4 4 ITA A en

If a car at rest accelerates uniformly to a speed of 144km h in 20s it covers distance of

uniform rope of length L and mass M lying on a smooth table is pulled by a constant force F What is the tension in the rope at a distance 1 from the end where the force is 1978 applied

3 40 cm 33 A block of mass 5 kg is placed on a surface with coefficient of friction 0 2 then the maximum and minimum value of force F for which the block remains at rest are g 10 m s Grethe 15 N N 150 100 TTT 1 15 N 10 N 3 10 N 25 N 5 kg 777777 50 2 25 N 5 N mg 4 5 N 25 N ff oks of

Laws of Motion A particle describes a horizontal circle of radius on the smooth surface of an inverted cone as shown The height of plane of circle above vertex is h The speed of particle should be 1 rg 2 2rg

58 A body of mass m is tied to a string of length I and is kept in a trolley The entire system is allowed to slide down on a smooth incline Calculate the pseudo force acting on the body if the observer is in the frame of trolley 1 mg sine 3 mg tane 2 mg cose 4 zero friction is

A man can just push a box on 37 concrete slope When he keeps it at the point where the angle increases to 53 he can just hold it from sliding back If the coefficient of friction between the box and 1 the concrete slope is u find tangent to the curve only Assume that the man is applying same magnitude of force along the 125 1 37 53

1 A truck moving at 36 km h 1 has to be brought to rest by applying brakes in such a way that there is no rela tive displacement of the goods in the truck with respect to the truck floor Coefficient of friction between the goods and the truck floor is 0 2 Find the minimum dis tance the truck must move before it comes to rest LOE E

C 9 MR2 2 if 0 45 The ring shown in the figure starts moving from rest with a constant horizontal acceleration ao g 3 Maximum deflection of the string from the vertical is 00 then A 0 30 B 0o 60 C at maximum deflection tension in string is equal to mg D at maximum deflection tension in string is equal to 2mg 3 Ring 3 Fixed smooth horizontal rail Particle

mass 80 kg stands on a horizontal weighing machine of negligible mass attached to a massless platform P that slides down at 37 incline The weighing machine reads 72 kg The man is always at rest w r t weighing machine Calculate P 37 Fig 7 145 a the vertical acceleration of the man

56 Blocks A and B are connected by a bar of negligible weight If m m 170 kg and 0 2 and Hg 0 4 where and are the coefficient of friction between blocks A and B and plane then the tension in the bar is tane 1 250 N 8 15 2 100 N

12 The pulleys and strings are smooth and mass For the system to remain in equilibrium the angle 0 should be m 2m m 2 30 4 60

5 A sphere of radius 25 cm and mass 1 kg is hung by a string of negligible mass and length 40 cm then tension in the string is 1 10 81 N 2 18 4 N 3 10 N 4 8 N R

49 Blocks shown in figure moves with constant velocity 10 m s towards right All surfaces in contact are rough The friction force applied by B on A is 1 ON 3 10 N 20 N A B 2 4 Ground 20 N Insufficient data

smooth pulley rigidly attached to trolley A If the speed The string shown in Fig 6 358 is passing over small and magnitude of acceleration of block B at the instant of trolley is constant and equal to v towards right speed shown in figure are A B 50 x 3 cm Fig 6 358 h 4 cm

A sphere of mass m is rotating between two inclined walls with a uniform angular velocity as sho figure If the coefficient of friction between each wall and the sphere is u Then the ratio of the friction forces f f offered by the walls 1 and 2 on the sphere will be A tan 2 B B tan 20 sin 20 cos 20 sin 9 u cose versi D cos 20

1 3 10N 53 Two wooden blocks are moving on a horizontal surface such that the mass m remains stationary with respect to block of mass M as Ishown in the figure The magnitude of force F is F TTI 1 M m g tane 3 ma cose Smooth M m 0 77 2 mg tane 4 M m g cosece ho 5

Calculate the minimum force applied for mass m stays at rest w r t the body of mass M 01 1 mg fr smooth M a m 2 Zero 3 m cannot be at relative rest

1 Two blocks A and B of masses 2 kg and 1 kg respectively are interconnected by a pulley string system as shown in the figure The system is released from rest and after the 1 kg block had descended through 1 m it attains a speed 0 4 m s The coefficient of friction between block A and the table is A 1 0 232 TI ad ll o B 2 0 461

84 A truck and a car are moving with velocity v towards each other They collide head in and stops after some time If the time of collision is 1 s which vehicle will have maximum change in momentum 1 Car 2 Truck None of these

A double inclined plane A is placed on a horizontal table and two blocks of masses m and m are placed on the two friction less inclined ma planes of A Fig 1 22 Two ends of a m 2 B m g A T mg m a m rope wound over a pulley Fig 1 22 are tied to the two blocks Find out the horizontal acceleration to be imparted to the system so that the blocks are at rest relative to A In this condition what will be the tension in the rope

Example 9 6 A bullet of mass 20 g is horizontally fired with a velocity 150 m s from a pistol of mass 2 kg What is the recoil velocity of the pistol

A block B of mass 10 kg is resting over a smooth horizontal plane Distance of B from the wall is 40 cm an it is held at rest by an inextensible thread BD Another thread is connected to left face of B and a block Ac mass 2 kg is suspended as shown in Fig Block C of mass 2 kg is resting against the vertical wall Blocks and C are hinged at the ends of a light rigid rod Assuming friction to be absent and when thread BD is burn 20 cm 20 cm Calculate the force developed in rod 40 cm 30 cm

3 A block of mass m is placed at relative equilibrium on an inclined plane which itself is placed on a lift moving upwards with constant velocity vo If the friction co efficient between block and plane is find the instantaneous power supplied by friction to the block 1 20 mgv Sin 20 2 mgv Sin 20 m vo 2 v mgSin 0

Find the value of acceleration a for which point x is exposed to air as shown in the figure 3g 1 39 4 2g 3 L X LTO 28 4 LMBE 2 A 4g 3 3g a

The kinetic energy of a particle increases continuously with time Then select correct alternative A the magnitude of its linear momentum is increasing continuously B its height above the ground must continuously decrease C the work done by all forces acting on the particle must be positive D the resultant force on the particle must be parallel to the velocity at all times

body of mass 10 kg is released on a roug inclined plane as shown in figure The reaction c the body by the plane is equal to 1 60 N 37 10 kg 0 8

tration 29 A truck pulls a mass of 1200 kg at a constant speed of 10 m s on a levelled road The tension in the coupling is 1000 N What is the power spent on the mass Find the tension when the truck moves up a road inclination 1 in 6 Solution

2 A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure 5 E4 Show that

24 A body of weight 2 kg is suspended as shown in the figure The tension T in the horizontal string in kgwt is U 2 1 3 3 2 3 30 T 2 1 2 kg wt 3 2 4 2

i ii iii figure The pulley is light The wedge is free to move on a frictionless surface A horizontal force F is applied on the system in such a way that m does not slide on M or both move together with some common acceleration Given M 2 m 0 Column I M Pseudo force acting on m as seen from the frame of Mis Pseudo force acting on M as seen from the frame of mis Normal force for 0 45 between m and Mis a b C Equal to F 5 36 PM Column II mF m M Greater than mF m M Less than mg sin 0 sin S

An electron and a proton are in a uniform electric field the ratio of their accelerations will a zero b unity Fe cythe ratio of the masses of proton and electron in order d the ratio of the masses of electron and proton in order

ision 6 A 1 kg block is given a velocity of 15 m s towards right over a very long rough plank of mass 2 kg as shown in figure 1 A P and p 2kg smooth The correct graph showing linear momentum of 1 kg i e p and of 2kg i e p versus time is P and p P and p 5 P B P and p P rough P Ikg P and p 15 m s C P P D

The two blocks m 5 kg and M 25 kg as shown in the figure are free to move The co efficient of friction between the blocks is us 0 4 but the co efficient of friction between ground and M is frictionless What is the minimum horizontal force F required to hold m against M F m M

15 The acceleration of block of mass M as shown in the figure is of system is released from rgt all the surfaces are smooth 1 3 M 2g 130 down the plane down the plane 2M 2 3 4 up the plane 2g up the plane

Two forces 4 N and F act at 120 with each other If their resultant is at right angles to 4 N the value of F is 1 4 N 2 6 N 3 8 N 4 12 N

A rocket in outer space has a payload of 15000 kg and 0 6 X10 kg of fuel The rocket can expel propellant at a speed of 12 km s Assume that the rocket starts from rest accelerates to its final velocity and then begins its trip How long will it take the rocket to travel a distance of 1 25X 105 km approximately the distance between Earth and Moon

In Fig 6 390 a block of mass m is released from rest when spring was in its natural length The pulley also has mass m but it is frictionless Suppose the value of m is such that finally it is just able to lift block M up after releasing it i ii iii iv Column I Weight of m required to just lift M Tension in the rod when m is in equilibrium Normal force acting on M when m is in equilibrium Tension in the string when displacement of m is maximum possible a C d Column II M 3 b Mg 2 M 2 8 8 2 mg Rod String Fig 6 390

Medical Q Bank 49 One end of massless rope which passes over a massless and frictionless pulley P is tied to a hook C The other end is free Maximum tension that the rope can bear is 640 N With what value of maximum acceleration in ms 2 can a man of 40 kg climb up the rope Take g 10 ms 2 1 16 C P 2 12

While working on a physics project at school physics lab you require a 4 F capacitor in a circuit across a potential difference of 1 kV Unfortunately 4 F capacitors are out of stock in your lab but 2 uF capacitors which can withstand a potential difference of 400 V are available in plenty If you decide to use the 2 F capacitors in place of 4 F capacitor minimum number of capacitors required are 1 16 3 20 2 18 4 12

16 A circuit contains an ammeter a battery of 30 V and a resistance 40 8 ohm all connected in series If the ammeter has a coil of resistance 480 ohm and a shunt of 20 ohm the reading in the ammeter will be Re AIPMT 2015 1 1 A 3 0 25 A 2 0 5 A 4 2 A

ABC is an equilateral triangle with O as its centre F F and F represent three forces acting along the sides AB BC and AC respectively If the total torque about O is zero then the magnitude of F is io A 1 F F 72 2 2 F F 3 F F 4 F F B F O F C

Two blocks A and B are kept on smooth surfaces having an acceleration a 3t m s and a 41 m s respectively Block C is attached to massless and frictionless pulley as shown in the figure Then at time 2 sec Initially assume system is at rest A velocity of block C will be 25 3 m s B velocity of block C will be 30 m s C acceleration of block C will be 11 m s D acceleration of block C will be 7 m s B

9 In the arrangement shown in the figure friction is absent everywhere The string and pulley are light The system is released from rest If acceleration of A is a then acceleration of B is a 1 a 3 a B A 2 2a 4 a C

From the top of a tower 100 m in height a ball is dropped and at the same time another ball is projected vertically upwards from the ground with velocity of 25 ms Find when and where the two balls will meet Take g 9 8 ms 1 2 Delhi 05 Ans 784 from top 4 s