R a r

I I T

y

For mu las at a Glance

Unit-I (Unit and Measurement)l Meter scale for distance from 10 3- to 10 2- m.l Vernier calliper for distance upto 10 4- m.l Screw gauge and spherometer for distance upto 10 5- m.

l Parallax method, q =b

D

l Distance of moon or planet, sb

=q

l Distance of planet from the Earth, sc t

=´

2

l Size of molecule, tnV

=400Å

cm, where c is speed of light in vacuum,

t is time interval, q is parallax angle, V is volume of a particle, b isthe length of an arc and D is distance between source and object.

l Conversion of one system of units into another for which we use

n nM

M

L

L

T

T

a b c

2 11

2

1

2

1

2

=é

ëê

ù

ûú

é

ëê

ù

ûú

é

ëê

ù

ûú

where, M L T1 1 1, , are fundamental units on one system, M L T2 2 2, , arefundamental units on other system. a b c, , are the dimensions of thequantity in mass, length and time, n1 is numerical value of thequantity in one system and n2 is its numerical value in the othersystem.l Sum, Z Z A A B B± = ± + ±D D D( ) ( )l Difference, Z Z A A B B± = ± - ±D D D( ) ( )

l Product, D D Dx

x

a

a

b

b= ± +

é

ëê

ù

ûú

l Quotient, D D Dx

x

a

a

b

b= ± +

é

ëê

ù

ûú

l Absolute error, D Saa

ni

nn

mean ==1

| |

l Relative error, daa

a=

D mean

mean

l Percentage error, % error = ´Da

amean

mean

100

l If xa b

c

n m

p= , then

D D D Dx

xn

a

am

b

bp

c

c= ± + +

é

ëê

ù

ûú, where ±Da, ± Db and

± Dc are absolute errors in a b, and c respectively.

Unit II (Ki ne mat ics)l Velocity-time relation, v u at= +

l Position-time relation, x x ut at= + +021

2l Position-velocity relation, v u as2 2 2= +

l Velocity, vds

dt=

l Acceleration, adv

dt=

l Displacement of the particle in nth sec ond, S ua

nn = + -2

2 1( )

l Instantaneous velocity, v Limx

dt

dx

dtin

t= =

®D

D

0

l Velocity of object A relative to object B, v v vAB A B= -l Velocity of object B relative to object A, v v vBA A B= -l Triangle law, R A B= +l Parallelogram law, R A B= +l Polygon law, R A B C D= + + +l Dot or scalar product, A B× = AB cos q

l Vector or cross product, A B n´ = AB sin $ql Addition of vectors, R A B AB= + +2 2 2 cos q

l Motion along horizontal direction,

x x u t a tn x= + +021

2 and x u t= cos q

l Time of flight T u g= 2 sin /q

l Motion along vertical direction, y y u t a tn y= + +021

2

y x g u x= - ´tan ( cos )q q1

2

2 2 2

l Maximum height of a projectile, Hu

g=

2 2

2

sin q

l Horizontal range of a projectile, Ru

g=

2 2

2

sin q

l Relation between w, f and T, wq

p= =t

f2

l Relation between v and w , v rdt

r= =Dq

w

l Lami’s theorem, F F F1 2 3

sin sin sina b g= =

where, u is initial velocity, v is final velocity, q is angular displacement, f is fre quency, w is an gu lar ve loc ity and r is dis place ment.

Unit III (Laws of Mo tion)l Newton’s second law, F a= ml Conservation of momentum, Fex = 0, then Dp = constantl Gravitational force, F mgg =l Weight, w mg=l Tension force , T mg= l Momentum, p v= ml Impulse, I F p p= ´ = -Dt 2 1

l Velocity ( )v of rocket, v um

me=

é

ëê

ù

ûúlog 0

l Thrust on the rocket, F udm

dt= -

é

ëê

ù

ûú

l When a lift moves upward with acceleration a, then R m g a= +( )l Lift moves downward, R m g a= -( )

where, m is mass of a body, g is acceleration due to gravity, u is initialvelocity and R is reaction force.

l Coefficient of static frictions (m ssf

R)

( )=

Limiting friction

Normal reaction

( )

l Coefficient of kinetic friction ( )( )

m Kkf

R=

Kinetic friction

Normal reaction

( )

l Circular motion of a car on level road, v rgsmax = m

l Motion of a car on a banked road, vrg s

s

max

( tan )

( tan )=

-

m q

m q1

l Angle of banking, q =æ

èçç

ö

ø÷÷

-tan 12v

rg

l Centrifugal force, Fmv

rmr= =

22w

l Acceleration of a body down a rough inclined plane a g= -(sin cos )q m q

l Work done in moving a body over a rough horizontal surface, W R s mg s= ´ = ´m m

l Work done in moving a body over a rough inclined plane, W mg s= + ´(sin cos )q m q