Solutions for Motion in a plane conceptual questions

1. c
2. a
3. d
4.a,b
5.a,b
6.d
7.b,c
8. a,b,c
9.a,b,d
10.a,b

Solution for Gravitation conceptual question

1.d
2.b
this can derived using kepler law T² =kR³
3.b
4.c
5.b
6.a,c
7.d
8.a
9.c
10.a

Conceptual question for Newton's law

1. when a Force is exerted on a body ,it can change
(a) Direction of motion
(b) Momentum
(c) Kinetic energy
(d) All the above

2. there are two statements
A Rate of change of momentum correspondes 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

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


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 > m₁ is 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 brfore block B

5. Which of the following observer is/are non interial
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

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


7.A IITJEE text book of mass M rests flat on a horizontal table of mass m placed on the ground.Let R_X->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 R_table->book
b. R_{ground->table} and mg+R_book->table
c. R_{ground->table} and R_{table->ground}
d Mg and R_table->book

8. Choose the correct alternative
a. The acceleration of a moving particle is always in the direction of its velocity
b. Velocity and acceleraion vectors of a moving particle may have any angle between 0 and 360 between them
c.Velocity and acceleraion 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


Solutions

Detailed Solutions
Ans 1:

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



Ans 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).


Ans 6

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

Ans 7.

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

Newtons law of Motion

Basic concepts of laws of motion

(1) Newton's first law of motion:-
'A body continues to be in state of rest or uniform motion unless it is acted upon by some external force to act otherwise'

(2) Newton's second law of motion:-
'Rate of change of momentum of a body is proportional to the applied force and takes place in the direction of action of force applied'
Mathematically,
F=dp/dt
=ma
where, F=external force applied
p=mv,momentum of the body
a=acceleration
SI unit of force is Newton (N).

(3) Impulse is the product of force and time which is equal to the change in momentum
Impulse=FΔt
=Δp

(4) Newton's third law of motion:-
'To every action there is always an equal and opposite reaction'
F_AB=-F_BA

(5) According to the law of conservation of linear momentum
Initial momentum = final momentum
m₁v1+m₂v2=m₁v1^'+m₂v2^'


For equilibrium of a body
F₁+F₂+F₃=0

Some points to note
1. An accelerated frame is called non interial frame while am non accelerated frame is called interial frame
2. Newton Ist law are valid in intertial frame only
3 Apparent weight of a body in the lift
Going Upward with acceleration a
W=m(g+a)
Going Down with acceleration a
W=m(g-a)
4.Always draw free body diagram to solve the force related problems

Thermodynamics objective solutions

Feb 6 Solutions

1. b
Hint:Workdone is area enclosed
2. b
Hint:Workdone is area enclosed
3.d
Hint:Workdone is area enclosed
4.a
5.d
6.c
7.d
8.b
9.c
hint for PVⁿ=constant,Molar Specific Heat=R/y-1 + R/1-n
10 a
hint for TV^y-1=constant

Feb 4 Solutions
1.a
dU=dQ-dW
2.d
3.d
4.a
hint V_rms=√3RT/M
5.b

Graphical Question for Kinematics

1. A ball is dropped vertically from a height h above the ground .It hits the ground and bounces up vertically to a height h/2.Neglecting subsequent motion and air resistance ,its velocity v varies with the height h as






















2. The displacement -time graph of a moving particle is shown below.The instantanous velocity of the particle is negative at the point









a. C
b. D
c. B
d. A

3.The velocity -time graph of a moving particle is shown below.Total displacement of the particle during the time interval when there is nonzero acceleration and retardation is










a. 60m
b. 40m
c. 50m
d. 30m

4. Figure below shows the displacement -time graph of two particles.Mark the correct statement about their relative velocity










a. It first increases and then decreases
b. It is a non zero constant
c. it is zero
d. none of the above

5.Four position -time graph are shown below.What all graph shows motion with positive velocities






















a. a and c only
b all the four
c. b and D only
d. b only

6. What all graph shows motion with negative velocities
a. b and d only
b all the four
c. a and c only
d. c only

7.which of the folliwing graph correctly represents velocity-time relationships for a particle released from rest to fall under gravity





















8.The v-x graph(fig1) of a particle moving along a straight line is shown below.Which of the following below graph(A,B,C,D) shows a-x graph
























Solutions

Relative velocity Conceptual questions

A. A gun is mounted on a train roof .Train is travelling with the velocity v in north direction.A car is also moving on a parallel track with train with velocity w in north direction.Two bullet are fired from the muzzle of the gun . Take north as positive and south as negative
1. Bullet one is fired in the north direction with the muzzle velocity u.Find the velocity of the bullet as seen from the observer on the earth
a u+v
b u-v
c u
d v

2. find the velocity of the bullet as seen from the observer on the moving car
a u+v-w
b u-v-w
c u
d v

3.Bullet one is fired in the south direction with the muzzle velocity u.Find the velocity of the bullet as seen from the observer on the earth
a u+v
b v-u
c u
d v

4.find the velocity of the second bullet as seen from the observer on the moving car
a u+v-w
b v-u-w
c u
d v

B.A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive
5.Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s

6. What is the velocty of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

7. find the velocty of ground with respect to monkey
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s

C.Two particles start from the origin of the horizontal x-y plane.Particle A moves along +x axis with uniform velocity u.Particle B moves along -y axis with velocity u. i and j are the unit vectors along x and y direction

8. find the relative velocity of particle B wrt to A at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above

9. find the relative velocity of particle A wrt to B at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above

10. find the relative position vector of particle A wrt to B at time t
a -ut(i+j)
b ut(i+j)
c. 0
d. None of the above


Solutions

Detailed Solutions

Ans 1
Velocity of bullet w.rt to train=u
Velcity of train=v
Velocity of bullet w.rt to train=Velocity of bullet w.r.t earth -Velocity of train w.r.t earth
So Velocity of bullet w.r.t earth =Velocity of bullet w.rt to train+Velocity of train w.r.t earth
=u+v



Ans 4.
Velocity of bullet w.rt to train=-u
Velcity of train=v
velocity of car
Velocity of bullet w.rt to car=Velocity of bullet w.r.t earth -Velocity of car w.r.t earth
= v-u-w


Ans 5
Velocity of train w.r.t to driver=Velocity of train w.r.t earth -Velocity of driver w.r.t earth
so =0

Ans 6
Given
velocity of train=15m/s
velocity of monkey w.r.t train=-5 m/s
Now velocity of monkey w.r.t train=-velocity of train w.r.t monkey
So velocity of train w.r.t monkey=5 m/s



Ans 8.

Velocity of A=ui
Velocity of B =-uj

Velocity of B w.r.t to A=Velocity of B-Velocity of A
=-u(i+j)

Ans 9

Velocity of A=ui
Velocity of B =-uj

Velocity of A w.r.t to B=Velocity of A-Velocity of B
=u(i+j)