NDA/NA NATIONAL DEFENCE ACADEMY NAVAL ACADEMY ENTRACE EXAMINATION

GENERAL SCIENCE PHYSICS | CHEMISTRY | BIOLOGY

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CONTENTS PHYSICS S.NO.

CHAPTER

PAGE NO.

1.

MEASUREMENT, MOTION AND FORCE

03-13

2.

WORK, ENERGY AND POWER

14-20

3.

CENTRE OF MASS AND ROTATIONAL MOTION

21-27

4.

GRAVITATION

28-48

5.

GENERAL PROPERTIES OF MATTER

49-60

6.

HEAT AND KINETIC THEORY OF GASES

61-69

7.

THERMODYNAMICS

70-84

8.

OPTICS

9.

OSCILLATION AND WAVES

109-126

10.

ELECTROSTATICS

127-138

11.

CURRENT ELECTRICITY

139-152

12.

MAGNETIC EFFECTS OF ELECTRIC CURRENT AND MAGNETISM

153-167

13.

NUCLEUS AND RADIOACTIVITY

168-174

14.

MODERN PHYSICS

175-186

85-108

CHEMISTRY S.NO.

CHAPTER

PAGE NO.

1.

PHYSICAL AND CHEMICAL CHANGES

189-195

2.

ELEMENTS, MIXTURES AND COMPOUNDS

196-204

3.

LAWS OF CHEMICAL COMBINATION AND GAS LAWS

205-214

4.

CONCEPT OF ATOMIC, MOLECULAR AND EQUIVALENT MASSES

215-223

5.

ATOMIC STRUCTURE AND RADIOACTIVITY

224-234

6.

PERIODIC CLASSIFICATION AND ELEMENTS

235-246

7.

CHEMICAL BONDING

247-253

8.

ACIDS, BASES AND SALTS

254-269

9.

OXIDATION, REDUCTION AND ELECTROCHEMISTRY

270-278

10.

NON-METALS AND THEIR COMPOUNDS

279-293

11.

SOME IMPORTANT CHEMICAL COMPOUNDS

294-306

BIOLOGY S.NO.

CHAPTER

PAGE NO.

1.

DIVERSITY IN LIVING WORLD

309-316

2.

CELL AND CELL DIVISION

317-322

3.

CONSTITUENTS OF FOOD (BIOMOLECULES)

323-326

4.

STRUCTURAL ORGANISATION AND PLANTS AND ANIMALS

327-333

5.

PLANTS PHYSIOLOGY AND REPRODUCTION

334-337

6.

HUMAN SYSTEM-I

338-343

7.

HUMAN SYSTEM-II

344-346

8.

HEALTH AND DISEASES

347-352

9.

ECONOMIC IMPORTANCE OF BIOLOGY

353-358

10.

ECOLOGY, BIODIVERSITY AND ENVIRONMENT

359-364

PHYSICS

.

.

.

1

CHAPTER

MEASUREMENT, MOTION & FORCE

1. Physical Quantities

2. Units

The quantities by means of which we describe the laws of physics are called physical quantities. A physical quantity is completely specified if it has (a) Magnitude only Ratio Refractive index, dielectric constant (b) Magnitude and unit Scalar Mass, charge, current (c) Magnitude, unit and direction Vector Displacement, torque. Physical quantity = Magnitude × unit 1.1 Quantities : These are of two types (a) Fundamental quantities (b) Derived quantities (a) Fundamental quantities : The quantities which do not depend upon other physical quantities are called fundamental quantities. There are of seven fundamental quantities in SI system(i) Mass (ii) Length (iii) Time (iv) Temperature (v) Electric current (vi) Luminous intensity (vii) Amount of substance These quantities are also called base quantities. (b) Derived quantities : The quantities which are derived with the help of fundamental quantities is called derived quantities as

2.1 That fixed and definite quantity which we take as our standard of reference and by which we measure other quantities of same kind, is defined unit. There are of two types.

Speed =

Dis tan ce Length = Time Time

(a) Fundamental Units (b) Derived Units (a) Fundamental Units : The units which are independent and which are not be derived from other units, are defined as fundamental units. e.g. The unit of mass, length, and time. There are seven fundamental units. (i) Unit of mass (ii) Unit of length (iii) Unit of time (iv) Unit of temperature (v) Unit of electric current (vi) Unit of luminous intensity (vii) Unit of amount of substance. (b) Derived Units The units of derived quantities are called derived units. e.g., Let us consider the unit of speed. speed = ∴

distance travelld time taken

Unit of Speed = =

Unit of distan ce unit of time

metre = ms–1 sec ond

Thus, the unit of speed is derived from fundamental units of length and time 2.2 Properties of Units : The unit of a physical quantity is inversely proportional to its numerical value. i.e. u ∝ 1/n where u and n are the units of physical quantity and its numerical value respectively. Relation between unit and its numerical value n1 u1 = n2 u2 Measurement, Motion, & Force | 3

2.3 Selection Criteria Of Units : (i) Selected unit must be universal, of proper size and magnitude (ii) Unit must be not affected by temperature, pressure and time. (iii) Easily definable and reproducible. 2.4 System Of Units Used : These are of Four types (i) C.G.S - (Centimeter - Gram - Second) system. (ii) M.K.S. - (Metre – Kilogram - Second) system (iii) F.P.S. - (Foot - Pound - Second) system (iv) S.I. - (System - international) system

3. Dimensions 3.1. Dimensions of a physical quantity are the powers to which the fundamental units of mass, length, time etc. must be raised in order to represent that physical quantity. Dimensional formula = [Ma Lb Tc Qd] where a, b, c, d are the dimensions of M, L, T, Q respectively. Some Points About Dimensions : (a) The dimensions of a physical quantity do not depend upon system of units to represent that physical quantity. (b) Pure numbers and pure ratio do not have any dimensions. i.e. these are dimension less, e.g. refractive index, relative density, relative permeability, cos θ, π, strain etc. (c) Similar dimension can be added or subtracted but it does not change the dimensions. 3.2. Uses of Dimension : The uses of dimension are as given below. (a) Homogeneity of dimensions in equation. (b) Conversion of units (c) Deducing relation among the physical quantities. 3.3. Limitations of the dimensional method : (a) First of all we have to know the quantities on which a particular physical quantity depends. (b) Method works only if the dependence is of the product type (Not applicable for x = ut + at2) (c) Numerical constants having no dimensions can not be deduce by the method of dimensions. (d) Method works only if there are as many equations available as there are unknowns.

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3.4 Some quantities Dimensions Example are given as (a) Gravitational constant G : Approach : From Newton's law of gravitation we have Fr 2 mm F = G 12 2 ⇒ G = m1m 2 r [G] =

[MLT −2 ][L2 ] [M] [M]

so its SI units is

m3 Nm 2 or kgs 2 kg 2

(b) Plank constant h : Approach : According to constant h : E E = hν ⇒ h = ν Substituting the dimensions of known physical quantities : [ML2 T −2 ] = M1L2T–1 T −1 (c) Coefficient of Viscosity η : Approach : According to Newton's law F ⇒ η= ⎛ dv ⎞ A⎜⎜ ⎟⎟ ⎝ dy ⎠

[h] =

Substituting the dimensional formulae of all other known physical quantities. [η] =

[MLT −2 ] [L2 ][LT −2 / L ]

In Electricity : (a) Current I : While dealing electricity we assume current to be a fundamental quantity and represent it by [A] with unit ampere (A) (b) Charge Q : Q As I= t So [Q] = [I] [t] ⇒ [Q] = [At] The SI unit of charge is A × s and is called coulomb (C). (c) Electric potential V : W It is defined as V = q

So

[V] =

[ML2 T −2 ] [AT]

i.e. [V] = [ML2 T–3 A–1] So SI unit of potential is J/C and is called volt (V) (d) Electric intensity E : It is defined as F E = q so

[E] =

[MLT −2 ] ⇒ [E] = [MLT–3 A–1] [AT]

So SI unit of electric intensity is Newton N−m → Coulomb c−m ⎡J

⎤

⎢ C =V ⎥ J V ⎣ ⎯⎯ ⎯ ⎯⎦ → c−m m (e) Capacitance C It is defined as q = CV

[ N −m =J ] ⎯⎯ ⎯ ⎯⎯→

i.e. C =

q V

⇒ [C] =

=

q2 W [as V = ] q W

2

[AT] = [M–1 L–2 T4 A2] [ML2 T −2 ]

and its unit coulomb / volt is called farad. (f) Permittivity of free space ε0 : According to coulomb's law 1 q1q 2 F = 4πε 0 r 2 ⇒ [ε0] =

[ q ]2 [A 2T 2 ] = [F][r ]2 [MLT −2 ][L2 ]

⇒ [ε0] = [M–1 L–3 T4 A2]

MOTION 1. Distance Distance is the actual length of the path. It is the characteristic property of any path i.e. path is always associated when we consider distance between two positions.

Distance between A and B while moving through path (1) may or may not be equal to the distance between A and B while moving through path (2)

2. Displacement Displacement of a particle is a position vector of its final position w.r.t. initial position. → Displacement = AB = (x2 – x1) iˆ + (y2 – y1) ˆj + (z2 – z1) kˆ It is the characteristic property of any point i.e. depends only on final and initial positions. Regarding distance and displacement it is worth noting that : (a) Distance is scalar, while displacement is vector both having same dimensions [L] and same SI unit metre. (b) The magnitude of displacement is equal to minimum possible distance so, Distance ≥ |Displacement| (c) For motion between two points displacement is single valued, while distance depends on actual path and so can have many values.

3. Speed It is the distance covered by the particle in one second. (i) It is a scalar quantity (ii) Unit : In M.K.S. Meter/Second or km/sec. In C.G.S. cm/sec (iii) Dimension : [M0L1T–1] (a) Instantaneous Speed : It is the speed of a particle at particular instant. ΔS dS Instantaneous speed = lim = Δt →0 Δt dt (b) Average speed=

Total distan ce Total time

(c) Uniform speed : If during the entire motion speed of the body remains same, the body is said to have uniform speed. (d) Non-uniform speed : If speed changes, the body is said to have non-uniform speed.

4. Velocity It is defined as rate of change of displacement. (i) It is a vector quantity (ii) Its direction is same as that of displacement Measurement, Motion, & Force | 5

(iii) Unit and dimension : Same as that of speed (a) Instantaneous Velocity : It is defined as the velocity at some particular instant. →

→

Δr dr Instantaneous velocity = lim = Δt →0 Δt dt (b) Average Velocity : Total displacement Average velocity = Total time

(c) Uniform velocity : A particle is said to have uniform velocity, if magnitudes as well as direction of its velocity remains same and this is possible only when the particles moves in same straight line reversing its direction. (d) Non-uniform velocity : A particle is said to have non-uniform velocity, if either of magnitude or direction of velocity changes (or both changes).

5. Motion with Uniform Acceleration Let u = Initial velocity (at t = 0), v = Velocity of the particle after time t a = Acceleration (uniform), s = Displacement of the particle during time 't' v−u [Because of uniform (a) Acceleration, a = t acceleration, this acceleration is instantaneous as well average acceleration]. From above equation ....(i) v = u + at (b) Displacement s = Average velocity × time, u+v s= t ....(ii) 2 [This is very useful equation, when acceleration is not given] (c) From (i) and (ii) ....(iii) s = u t + (1/2) a t2 Again from (i) and (iii)

6. Motion Under Gravity (i) The acceleration is constant, i.e. →

→

a = g = 9.8 m/s2

and directed vertically downwards. (ii) The motion is in vacuum i.e. viscous force or thrust of the medium has no effect on the motion. 6.1 Body Falling Freely Under Gravity : Taking initial position as origin and direction of motion (i.e. downward direction) as positive, here we have u = 0 (as body starts from rest) a=+g (as acceleration is in the direction of motion) So, if the body acquires velocity v after falling a distance h in time t, equations of motion viz v = u + at ⎛1⎞ s = ut + ⎜ ⎟ at2 ⎝2⎠ v 2 = u2 + 2as reduces to v = gt ....(1) ⎛1⎞ h = ⎜ ⎟ gt2 ....(2) ⎝2⎠

and

....(3) v 2 = 2 gh These equations can be used to solve most of the problems of freely falling as t is given From eq. (1) & (2) v = gt

and h =

1 2 gt 2

h is given From eq. (2) & (3) t=

2h g

v=

2gh

v is given From eq. (3) & (1) t=

v g

h=

v2 2g

s = vt − (1 / 2) at 2

[Here negative sign does not indicate that retardation is occurring] .....(iv) (d) From (i) and (ii) v 2 = u 2 + 2 a.s th sn = displacement of particle in n second = sn – sn −1 = { u (n) + (1/2) a n2} – { u (n –1) + (1/2) a (n – 1)2} sn = u + 1/2 a (2n – 1)

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6.2 Body is projected vertically up : Taking initial position as origin and direction of motion (i.e. vertically up) as positive, here we have v = 0 [as at the highest point, velocity = 0], a = – g [as acceleration is downwards while motion upwards]. So, if the body is projected with velocity u and reaches the highest point at a distance h above the ground in time t, the equations of motion viz

v s v2 0 h 0 u h

and

and or (∵ u = gt),

u2 = 2 gh

if t is given From eq. (1) & (2) u = gt h = 1/2 gt2

if h is given From eq. (2) t=

PROJECTILE MOTION

= u + at = ut + 1/2 at2 = u2 + 2as reduces to = u – gt = ut – 1/2 gt2 = u2 – 2gh = gt ....(1) ....(2) = 1/2 gt2

Introduction

....(3)

2h / g

if u is given From eq. (3) t = u/g

2hg

h = u2/2g

u=

(i) Any particle, which once thrown, moves freely in gravitational field of the earth, is defined as a projectile. (ii) It is an example of two dimensional motion with constant acceleration. (iii)Parabolic motion can be considered as two simultaneous motions in mutually perpendicular directions viz. (a) Horizontal and (b) Vertical Projectile Thrown From The Ground Level (i) The particle is thrown from the ground level at an angle θ from the horizontal velocity u.

7. Relative - Velocity (i) There is nothing in absolute rest or absolute motion. (ii) Motion is a combined property of the object under study and the observer. (iii)Relative motion means, the motion of a →

body with respect to another. Now if V A →

and V B are velocities of two bodies relative to earth, the velocity of B relative to A will be given by →

→

→

(ii) Initial velocity can be resolved into two components u cosθ = Horizontal component u sinθ = Vertical component Velocity at a general point P(x, y) : v=

v 2x + v 2y

The direction of v from horizontal tan

V BA = V B – V A

Note : (a) If two bodies are moving along the same line in same direction with velocities VA and VB relative to earth, the velocity of B relative to A will be given by VBA = VB – VA. If it is positive the direction of VBA is that of B and if negative the direction of VBA is opposite to that of B. (b) However, if the bodies are moving towards or away from each other, as direction of VA and VB are opposite, velocity of B relative to A will have magnitude VBA = VB – (–VA) = VB + VA and directed towards A or away from A respectively.

α=

vy

vx Trajectory equation : y = u sin θ t – (1/2) gt2 and x = (u cos θ) t From these equations, (eliminating t) g x2 y = x tan θ – 2 2u cos2 θ The maximum height reached by the projectile : 2 u 2 sin 2 θ u y = (uy = vertical velocity) 2g 2g Time of flight of the projectile :

h0 =

Measurement, Motion, & Force | 7

Time taken to reach max. height u sin θ t= (using v = u + gt) g The time interval from initial launch of projectile upto its return to the ground level is known as the time of flight (T) of projectile 2u y 2u sin θ = T = g g where uy = vertical velocity Horizontal Range of The Projectile : The horizontal distance covered by the projectile during its time of flight is known as the horizontal range of the projectile R = (using v2 = u2 + 2gh) (i) For maximum range, θ = 45º ∴ Rmax = u2/g In this situation

(i) It is a vector quantity (ii) In vector form =–

mv 2 mv 2 . rˆ = – r r2

→

r

Type of Circular Motion (a) Uniform circular motion (b) Non Uniform Circular Motion : (a) Uniform Circular Motion : If m = mass of body, r = radius of circular orbit, v = magnitude of velocity ac = centripetal acceleration, at = tangential acceleration In uniform circular motion : →

→

→

(i) | v1 | = | v2 | = | v3 | = constant i.e. speed is constant → v2

CIRCULAR MOTION

→ v1

Centripetal Acceleration and Centripetal Force (i) A body or particle moving in a curved path always moves effectively in a circle at any instant. (ii) The velocity of the particle changes moving on the curved path, this change in velocity is brought by a force known as centripetal force and the acceleration so produced in the body is known as centripetal acceleration. (iii)The direction of centripetal force or acceleration is always towards the centre of circular path. Expression for Centripetal Acceleration v v2 v= = rω2 r r Expression for Centripetal force If v = velocity of particle, r = radius of path Then necessary centripetal force Fc = mass × acceleration

ac =

Fc = m

v2 r →

v

→ Fc →

v

→ → Fc → Fc → Fc

v

→

v

This is the expression for centripetal force

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| NDA/NA (Physics)

→ v3 →

(ii) As | v | is constant so tangential acceleration at = 0 ac

(iii)

at = 0 Tangential force Ft = 0 Fc

Ft = 0 (iv)Total acceleration v2 a = a 2c + a t 2 = ac = (towards the centre) r (b) Non-uniform Circular Motion : In this tangential acceleration at ≠ 0 (i) ac = centripetal acceleration

⇒ ac =

F v2 = ω2r = c r m

tangential acceleration a t = (ii) Net acceleration, a

=

a c2 + a 2t =

Fnet m

dv dt

The angle made by 'a' with ac, tan θ =

at F = t ac Fc

θ

ac θ

ac

When two bodies A and B exert force on each ⎛→ ⎞ other, the force (action) of A on B ⎜⎜ FBA ⎟⎟ , is ⎠ ⎝ always equal and opposite to the force of → → ⎛→ ⎞ B on A ⎜⎜ FAB ⎟⎟ . Thus FAB = – FBA ⎠ ⎝

Impulse

a1

→

NEWTON'S LAWS OF MOTION & FRICTION

of the body respectively

1. First Law of Motion

Thus impulse of force = F Δt = Δ p = p f – p i

→

Acoording to this law, every body continues in its state of rest or motion in a straight line unless it is compelled by external force to change that state. (i) This law is also called law of inertia. Inertia is a virtue by which a body opposes the state of rest or motion. (ii) Force is such a factor, which is essential for change in translatory motion of a body. (iii)The first law of motion defines the force.

2. Second Law of Motion According to this law, the rate of change of momentum (mass × velocity) of a body is proportional to the impressed force and it takes place in the direction of the force.

→

→

F ∝

→

dp dt

→

→

→

F =m a

→

(a) If we slide or try to slide a body over a surface the motion is resisted by a bonding between the body and the surface. This resistance is represented by a single force and is called friction. (b) The force of friction is parallel to the surface and opposite to the direction of intended motion.

2. Graphical Representation of Friction Variation with Applied Force Limiting Friction

a St

t ric F tic

n io

Dynamic Friction

Applied force F →

In scalar form, F = ma (i) Force is a vector quantity, whose unit is Kg.m (In MKS) Newton or sec 2 and Dyne or

→

1. Friction and Frictional Force

fmax = μsR

dp dp F =k = dt dt

→

→

FRICTION

Friction f →

Mathematically

→

When pi and pf are initial and final momenta

gm × cm sec 2

(In C. G. S.)

(ii) The dimension of force is [MLT–2] (iii) The second law of motion gives the magnitude and unit of force.

3. Third Law of Motion According to this law, 'Every action has its equal and opposite reaction"

3. Types of frictional force and their definition There are four types of frictional force 1. Static friction 2. Dynamic friction and Sliding friction Static friction (a) The frictional force which is effective before motion starts between two planes in contact with each other, is known as static friction. Dynamic friction (μK) (a) If the applied force is increased further and sets the body in motion, the friction opposing the motion is called dynamic or kinetic friction. Measurement, Motion, & Force | 9

EXERCISE Q.1

The dimensional formula for magnetic flux is(A) M1L1T2A–1 (B) M1L2T2A–1 (C) M1L2T–2A–1 (D) M2L1T–2A1

Q.2

Following pair of quantities have same dimensions: (A) potential energy and torque (B) power and velocity (C) potential energy and gravitational constant (D) force and velocity

Q.3

One nanometer is equal to (A) 109 mm (B) 10–6 cm –7 (C) 10 cm (D) 10–9 cm

Q.4

For any coil the work done for a current ‘i’ is given by Li2, then dimensions of Li2 are : (A) M1L2T–2 (B) M2L2T–2 (C) ML–1T (D) can not be expressed in M, L, T

Q.5

If A and B have different dimensions then the correct relation according to dimensional principles will be : (A) A + B (B) A – B (C) A/B (D) eA/B

Q.6

A particle moves from the position of rest and attains a velocity of 30 m/sec after 10 sec. The acceleration will be (A) 9 m/sec2 (B) 18 m/sec2 2 (C) 3 m/sec (D) 4 m/sec2

Q.7

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is (A) 1 m/sec (B) 10 m/sec (C) 5 m/sec (D) 2m/sec

Q.9

A train is moving in the north at a speed 10m/sec. Its length is 150m. A parrot is flying parallel to the train in the south with a speed of 5m/s. The time taken by the parrot to cross the train will be : (A) 12sec (B) 8sec (C) 15sec (D) 10sec

Q.10

A body starts from rest, the ratio of distances travelled by the body during 3rd and 4th seconds is : (A) 7/5 (B) 5/7 (C) 7/3 (D) 3/7

Q.11

The linear momentum of a body is p. The linear momentum p varies with time. The equation for variation is p = a + bt2 where a and b are constants. The effective force acting on the body is (A) proportional to t2 (B) constant (C) proportional to t (D) inversely proportional to t

Q.12

If the displacement of a particle is proportional to square of time, its motion is (A) nonuniformly accelerated (B) uniformly accelerated (C) With a uniform velocity (D) with a nonuniform acceleration but constant speed

Q.13

A particle has velocity given by v = 20 + 0.1 t2 then it has (A) uniform acceleration (B) uniform retardation (C) non uniform acceleration (D) zero acceleration

The displacement-time graph for two particles A and B are straight lines inclined at angles of 30° and 60° with the time axis. The ratio of the velocities VA and VB is -

(A) 1 : 2

10

Q.8

(B) 1 :

| NDA/NA (Physics)

3 (C)

3 : 1 (D) 1 : 3

Q.14

The initial velocity of a body moving along a straight line is 7m/s . It has a uniform acceleration of 4m/s2. The distance covered by the body in the 5th second of its motion is – (A) 25 m (B) 35 m (C) 50 m (D) 85 m

Q.15

The velocity time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 sec are respectively

(A) 8m, 16m (C) 16m, 16m Q.16

Q.17

Q.18

(B) 16m, 8m (D) 8m, 8m

At the top of the trajectory of a projectile the direction of its velocity and accleration are(A) Parallel to each other (B) inclined at an angle of 45º to the horizontal to the (C) Perpendicular to each other (D) None of the above statement is correct Three particles A, B and C are projected from the same point with same intial speeds making angles 30º , 45º and 60º respectively with the horizontal . Which of the following statement is correct ? (A) A, B and C have equal ranges (B) ranges of A and C are equal and less than that of B (C) ranges of A and C are equal and greater than that of B (D) A, B and C have equal ranges A hunter aims the gun and fires a bullet directly towards a monkey sitting at a distant tree. To save itself, monkey can (A) either sit at the position or drop downward (B) either sit at the position or jump upward (C) either jump upward or drop downward (D) nothing can be said

Q.19

The kinetic energy of a projectile at the highest point is (A) zero (B) maximum (C) minimum (D) equal to total energy

Q.20

A bomb is fired from a cannon with a velocity of 1000m/s making an angle of 30º with the horizontal. What is the time taken by the bomb to reach the highest point ? (A) 11sec (B) 23 sec (C) 38 sec (D) 51 sec

Q.21

The angle of projection of a body is 15º . The other angle for which the range is the same as the first one is equal to(A) 30º (B) 45º (C) 60º (D) 75º

Q.22

A particle is projected such that the horizontal range and vertical height are the same. Then the angle of projection is(B) tan–1 (4) (A) π/4 (C) tan–1 (3)

(D) π/3

Q.23

The horizontal and verticle distances travelled by a particle in time t are given by x = 6t and y = 8t – 5t2. If g = 10m/sec2, then the initial velocity of the particle is(A) 8 m/sec (B) 10 m/sec (C) 5 m/sec (D) zero

Q.24

A bullet fired from a gun at sea level rises to a maximum height of 5km when fired at a ship 20 km away. If the bullet hits the ship then the muzzle velocity should be(A) 7 m/sec (C) 28 m/sec

Q.25

(B) 200 5 m/sec (D) 56 m/sec

The maximum range of a gun on a horizontal terain is 16 km. If g = 10 m/sec2 , the muzzle velocity of the shell must be(A) 400 m/sec

(B) 160 10 m/sec

(C) 1600 m/sec

(D) 200

2 m/sec

Measurement, Motion, & Force | 11