Chapter 5 - LAWS OF MOTION

A rectangular box lies on a rough inclined surface. The co-efficient
of friction between the surface and the box is μ. Let the mass of the
box be m.
(a) At what angle of inclination θ of the plane to the horizontal will
the box just start to slide down the plane?
(b) What is the force acting on the box down the plane, if the angle
of inclination of the plane is increased to α > θ ?
(c) What is the force needed to be applied upwards along the plane
to make the box either remain stationary or just move up with
uniform speed?
(d) What is the force needed to be applied upwards along the plane
to make the box move up the plane with acceleration a?

A cricket bowler releases the ball in two different ways
(a) giving it only horizontal velocity, and
(b) giving it horizontal velocity and a small downward velocity.
The speed vs at the time of release is the same. Both are released
at a height H from the ground. Which one will have greater speed
when the ball hits the ground? Neglect air resistance.

When a body slides down from rest along a smooth inclined plane
making an angle of 45° with the horizontal, it takes time T. When
the same body slides down from rest along a rough inclined plane
making the same angle and through the same distance, it is seen
to take time pT, where p is some number greater than 1. Calculate
the co-efficient of friction between the body and the rough plane.

A 100 kg gun fires a ball of 1kg horizontally from a cliff of height
500m. It falls on the ground at a distance of 400m from the bottom
of the cliff. Find the recoil velocity of the gun.

A block of mass M is held against a rough vertical wall by
pressing it with a finger. If the coefficient of friction between
the block and the wall is μ and the acceleration due to
gravity is g, calculate the minimum force required to be
applied by the finger to hold the block against the wall ?

In the above given problem if the lower thread is
pulled with a jerk, what happens?

A woman throws an object of mass 500 g with a speed of 25 m s1.
(a) What is the impulse imparted to the object?
(b) If the object hits a wall and rebounds with half the original speed,
what is the change in momentum of the object?

Why does a child feel more pain when she falls down on a hard
cement floor, than when she falls on the soft muddy ground in the
garden?

Why does a child feel more pain when she falls down on a hard
cement floor, than when she falls on the soft muddy ground in the
garden?

A block placed on a rough horizontal surface is pulled by a
horizontal force F. Let f be the force applied by the rough surface
on the block. Plot a graph of f versus F.

A person driving a car suddenly applies the brakes on seeing a
child on the road ahead. If he is not wearing seat belt, he falls
forward and hits his head against the steering wheel. Why?

A girl riding a bicycle along a straight road with a speed of 5 m s–1
throws a stone of mass 0.5 kg which has a speed of 15 m s–1 with
respect to the ground along her direction of motion. The mass of
the girl and bicycle is 50 kg. Does the speed of the bicycle change
after the stone is thrown? What is the change in speed, if so?

(a) Define impulse. State its S.I. unit?
(b) State and prove impulse momentum theorem?

A train runs along an unbanked circular bend of radius 30m at a speed of 54km/hr.
The mass of the train is 106kg. What provides the necessary centripetal force
required for this purpose? The engine or the rails? What is the angle of banking
required to prevent wearing out of the rail?

A shell of mass 0.020kg is fired by a gun of mass 100kg. If the muzzle speed of the
shell is 80m/s, what is the recoil speed of the gun?

Two blocks of masses m₁, m₂ are connected by light spring on a smooth horizontal

surface. The two masses are pulled apart and then released. Prove that the ratio of

their acceleration is inversely proportional to their masses.

Give the magnitude and direction of the net force acting on
(a) A drop of rain falling down with constant speed.
(b) A kite skillfully held stationary in the sky.

What provides the centripetal force to a car taking a turn on a level road?

Name the factor on which coefficient of friction depends?

State Newton’s second, law of motion. Express it mathematically and hence obtain
a relation between force and acceleration.

How is centripetal force provided in case of the following?
(i) Motion of planet around the sun,
(ii) Motion of moon around the earth.
(iii) Motion of an electron around the nucleus in an atom.

Write two consequences of Newton’s second law of motion?

An elevator weighs 3000kg. What is its acceleration when the in the tension

supporting cable is 33000N. Given that g = 9.8m/s².

Force of 16N and 12N are acting on a mass of 200kg in mutually perpendicular
directions. Find the magnitude of the acceleration produced?

A force is being applied on a body but it causes no acceleration. What possibilities
may be considered to explain the observation?

Friction is a self adjusting force. Justify. [

Why does a swimmer push the water backwards?

Why is it desired to hold a gun tight to one’s shoulder when it is being fired?

A particle of mass 0.40 kg moving initially with constant speed of 10m/s to the
north is subject to a constant force of 8.0 N directed towards south for 30s. Take at
that instant, the force is applied to be t = 0, and the position of the particle at that
time to be x = 0, predict its position at t = -5s, 25s, 30s?

A monkey of mass 40 kg climbs on a rope which can stand a maximum tension 600

N. In which of the following cases will the rope break? The monkey (a) climbs up

with an acceleration of 6m/s² (b) climbs down with an acceleration of 4m/s² (c)

climbs up with a uniform seed of 5m/s (d) falls down the rope freely under gravity.

Take g = 10m/s² and ignore the mass of the rope.

How does banking of roads reduce wear and tear of the tyres?

Why does a cyclist lean to one side, while going along curve? In what direction does
he lean?

A bird is sitting on the floor of a wire cage and the cage is in the hand of a boy. The
bird starts flying in the cage. Will the boy experience any change in the weight of
the cage?

Action and reaction forces do not balance each other. Why?

Which of the following is scalar quantity? Inertia, force and linear momentum.

A thief jumps from the roof of a house with a box of weight W on his head. What
will be the weight of the box as experienced by the thief during jump?

Ten one rupee coins are put on top of one another on a table. Each coin has a mass
m kg. Give the magnitude and direction of
(a) The force on the 7th coin (counted from the bottom) due to all coins above it.
(b) The force on the 7th coin by the eighth coin and
(c) The reaction of the sixth coin on the seventh coin.

(a) State impulse – momentum theorem?
(b) A ball of mass 0.1kg is thrown against a wall. It strikes the wall normally with
a velocity of 30m/s and rebounds with a velocity of 20m/s. calculate the
impulse of the force exerted by the ball on the wall.

A man weighs 70kg. He stands on a weighting machine in a lift, which is moving

(a) Upwards with a uniform speed of 10m/s.

(b) Downwards with a uniform acceleration of 5m/s².

(c) Upwards with a uniform acceleration of 5m/s². Take g = 9.8m/s².

What would be the readings on the scales in each case what would be the

reading if the lift mechanism failed and it came down freely under gravity?

Explain why passengers are thrown forward form their seats when a speeding bus
stops suddenly.

A nucleus is at rest in the laboratory frame of reference. Show that if it
disintegrates into two smaller nuclei, the products must be emitted in opposite
directions.

Two billiard balls each of mass 0.05kg moving in opposite directions with speed
6m/s collide and rebound with the same speed. What is the impulse imparted to
each ball due to other.

A soda water bottle is falling freely. Will the bubbles of the gas rise in the water of
the bottle?

A lift is accelerated upward. Will the apparent weight of a person inside the lift
increase, decrease or remain the same relative to its real weight? If the lift is going
with uniform speed, then?

The two ends of spring – balance are pulled each by a force of 10kg.wt. What will
be the reading of the balance?

If force is acting on a moving body perpendicular to the direction of motion,
then what will be its effect on the speed and direction of the body?

A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for ω ≤√g/R. What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √2g/R? Neglect friction.

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

 You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death-well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

 A disc revolves with a speed of 100 / 3 rev / min, and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record?

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s^–2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

 A block of mass 15 kg is placed on a long trolley. The coefficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 m s^–2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, (b) an observer moving with the trolley.

  Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid wall (Fig. 5.21). The coefficient of friction between the bodies and the table is 0.15. A force of 200 N is applied horizontally to A. What are (a) the reaction of the partition (b) the action-reaction forces between A and B? What happens when the wall is removed? Does the answer to (b) change, when the bodies are in motion? Ignore the difference between μ_sand μ_k.

A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of 6 m s^–2
(b) climbs down with an acceleration of 4 m s^–2
(c) climbs up with a uniform speed of 5 m s^–1
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).

A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig. 5.19. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?

 A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 10⁶ kg. What provides the centripetal force required for this purpose – The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

. An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?

Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of
(a) the force on the 7^th coin (counted from the bottom) due to all the coins on its top,
(b) the force on the 7^th coin by the eighth coin,
(c) the reaction of the 6th coin on the 7^th coin.

 A stream of water flowing horizontally with a speed of 15 m s^–1 gushes out of a tube of cross-sectional area 10^–2 m², and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]

T₁ and V₁ denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point.

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^–2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.) 

 Explain why
(a) a horse cannot pull a cart and run in empty space,
(b) passengers are thrown forward from their seats when a speeding bus stops suddenly,
(c) it is easier to pull a lawn mower than to push it,
(d) a cricketer moves his hands backwards while holding a catch.

 If, in Exercise 5.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:
(a) the stone moves radially outwards,
(b) the stone flies off tangentially from the instant the string breaks,
(c) the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

 A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

 Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for t < 0, t > 4 s,0 < t < 4 s? (b) impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only).

A man of mass 70 kg stands on a weighing scale in a lift which is moving 
(a) upwards with a uniform speed of 10 m s^–1,
(b) downwards with a uniform acceleration of 5 m s^–2,
(c) upwards with a uniform acceleration of 5 m s^–2.
What would be the readings on the scale in each case?
(d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^–1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

A truck starts from rest and accelerates uniformly at 2.0 m s^–2. At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 11 s? (Neglect air resistance.)

A body of mass 0.40 kg moving initially with a constant speed of 10 m s^–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.

The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^–1 to 3.5 m s^–1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms^–1. How long does the body take to stop?

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is:
(i) T, (ii) T - mv² / l, (iii) T + mv² / l, (iv) 0
T is the tension in the string. 
[Choose the correct alternative]. 

 Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,
(a) just after it is dropped from the window of a stationary train,
(b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
(c) just after it is dropped from the window of a train accelerating with 1 m s^-2,
(d) lying on the floor of a train which is accelerating with 1 m s^-2, the stone being at rest relative to the train. Neglect air resistance throughout.

A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,
(a) during its upward motion,
(b) during its downward motion,
(c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45° with the horizontal direction?
Ignore air resistance.

 Give the magnitude and direction of the net force acting on
(a) a drop of rain falling down with a constant speed,
(b) a cork of mass 10 g floating on water,
(c) a kite skillfully held stationary in the sky,
(d) a car moving with a constant velocity of 30 km/h on a rough road,
(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.