 # Laws Of motion Examples with solutions

## Solved Examples

Question 1 Force exerted on a body changes it's

(a) Direction of motion
(b) Momentum
(c) Kinetic energy
(d) All the above

Solution: A body acted upon by a certain force produces acceleration i.e. it undergoes change in it's velocity. hence choice (d) is correct

Question 2 there are two statements
A Rate of change of momentum corresponds to force
B Rate of change of momentum corresponds to Kinetic Energy
Which of the following is correct

(a) A only
(b) B only
(c) Both A and B are correct
(d) Both A and B are wrong

Solution

F=dp/dt so a is correct

Question 3 A truck and car are moving on a plane road with same kinetic Energy. They are brought to rest by application of brakes which provide equal retarding forces. Which of the following statements is true.

(a) Distance traveled by truck is shorter then car before coming to rest
(b) Distance traveled by car is shorter then truck before coming to rest
(c) Distance traveled depends on individual velocity of both the vehicles
(d) Both will travel same distance before coming to rest

Solution 3
By work energy theorem we know
KEf-KEi=Workdone

So in this case
Initial KE=retarting force * distance traveled

Since kinetic energy is same and retarding force is equal

Distance traveled will be same

Question 4 A block A of mass m1 is released from top of smooth inclined plane and it slides down the plane. Another block of mass m2 such that m2 > m1is dropped from the same point and falls vertically downwards. Which one of the following statements will be true if the friction offered by air is negligible?

(a) Both blocks will reach ground at same time
(b) Both blocks will reach ground with the same speed
(c) speed of both the blocks when they reach ground will depend on their masses
(d) Block A reaches ground before block B

Solution 4

since velocity of block when it reaches the ground is given by v=(2gh)1/2 and it is independent of the mass the correct choice will be (b).

Question 5 Which of the following observer is/are non inertial
a.A child revolving in the merry ground
b. A driver in a train moving with constant velocity v
c. A passenger in a bus which is slowing down to a stop
d None of these

Solution 5

Since centripetal acceleration is present in merry round it is non inertial frame of reference

Since bus is slowing down to a stop,it means it is experiencing a retardation ,so it is non inertial frame of reference

Question 6 there are two statements
A Newtons first law in valid from the pilot in an aircraft which is taking off
B Newtons first law in valid from the observer in a train moving with constant velocity
Which of the following is correct

(a) A only
(b) B only
(c) Both A and B are correct
(d) Both A and B are wrong

Solution 6

We know that Newtons law is invalid in Non inertial frame of reference, now since acceleration is present in Ist case..So answer is B

Question 7A IITJEE text book of mass M rests flat on a horizontal table of mass m placed on the ground.Let RX->Y be the constant force exerted by the body x on body Y.According to Newton third law,which of the following is an action-reaction pair of forces?

a. (M+m)g and Rtable->book
b. Rground->table and mg+Rbook->table
c. Rground->table and Rtable->ground
d Mg and Rtable->book

Solution 7

Action reaction pair acts on different body and always are in opposite direction.We will have to draw free body diagram for each part in this case.

Question 8 Choose the correct alternative
a. The acceleration of a moving particle is always in the direction of its velocity
b. Velocity and acceleration vectors of a moving particle may have any angle between 0 and 360 between them
c.Velocity and acceleration vectors of a moving particle may have any angle between 0 and 180 between them
d. If the acceleration vector is always perpendicular to the velocity vector of a moving particle, the velocity vector does not change

Solution 8

In circular motion, acceleration vector is perpendicular to velocity and velocity is also changing.

Now acceleration and velocity can have any angle between

Question 9 there are two statements
A Newtons first law in valid from the pilot in an aircraft which is taking off
B Newtons first law in valid from the observer in a train moving with constant velocity
Which of the following is correct

(a) A only
(b) B only
(c) Both A and B are correct
(d) Both A and B are wrong

Solution 9 Newtons law is valid from Inertial frame of Reference
when the plane is taking off, it has acceleration so it can not be intertial frame of refrence
When the observer is train moving with constant velocity, so no acceleration is involved.So it is Inertial frame.Hence Newton law is valid

Question 10.A body of mass 5 kg starts from the origin with an initial velocity u=30i+40j m/sec.If the constant force acts on the body F=-(i+5j) N.The time in which y component of the velocity becomes zero is
a. 5 sec
b. 80 sec
c. 20 sec
d. 40 sec

Solution 10.

Force=-(i+5j) N
Mass =5 Kg
intial velocity u=30i+40j m/sec

Acceleration:-
a=F/m=-(i+5j)/5=-.2i-j

Y component of intial velocity is 40 m/s
Acceleration in that direction -1 m/s2

So
v=u+at
0=40-1t
or t=40 sec

Hence d is correct

Question 11.A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle.The motion of the particle takes place in a plane.it follows that
a. velocity is constant
b. acceleration is constant
c. KE is constant
d. Particle moves in a circular path

Solution 11
Since force is always perpendicular to the body, work done by it will be zero
So kinetic energy is constant
It is the case of uniform circular motion
Velocity magnitude is constant but direction is constantly changing
Acceleration is constant but direction is constantly changing

Hence c and d are constant

Question 12A small mass m is suspended from one end of a vertical string. and then whirled in a horizontal circle at a constant speed v.
Which of the followings is true
a.The strings stays vertical
b.The string becomes inclined to the vertical.
c.There is no force on mass m except its weight
d.The angle of inclination of the string does not depend on the v
e.The centripetal force on m is mg

Solution 12
Since the body is rotating on a horizontal circle,String will be inclined to the horizontal
It is shown in figure

The forces acting on the body are weight and tension in the string
Vertical component of the tension will balance out the weight of the body
Horizontal component will provide the required centripetal force for the circular motion

if T is the tension and W be the weight and θ be the angle of inclination
then
Tcosθ =Wg
And Tsinθ =mv2/R

So angle of inclination depends on the speed of the motion
So only correct answer is b

Question 13.The tension in cable supporting an elevator is equal to th weight of the elevator.The elevator may be
a. going up with increasing speed
b. going down with increasing speed
c. going up with uniform speed
d. going down with uniform speed.

Solution 13
Since the tension is the string equals weight of the elevator,It means resultant force is zero
So acceleration must be zero
Hence c and d are correct answer

Question 14 A reference frame attached to the earth
a.is an inertial frame by definition
b.cannot be inertial frame as earth is revolving around the sun
c.is an inertial frame because Newton's law are applicable in this frame
d.cannot be inertial frame because earth is rotating about its own axis

Solution 14
Earth cannot be inertial frame as it is revolving around the sun and also rotating about its axis

Question 15By means of rope ,a body of weight W is moved vertically upward with constant acceleration a .Find the tensile force in the rope
a. W(1+a/g)
b W(1-a/g)
c W
d. none of the above

Solution 15
Forces acting on the body
Tensile force vertically upward=S
Weight of the body vertically downward=W
Body has acceleration a vertically upwards

Net force on the body must provide the acceleration
so S-W=(W/g)a
or S=W(1+a/g) 