Document Text Contents
Page 1
RESONANCE KVPY_BIOMOLECULES-1 # 1
BIOMOLECULES-1
INTRODUCTION :
Living matter of cell is called protoplasm.
Protoplasm (Gr. Protos-first+ Plasma-organization) is a living organized substance which is the place
for all physical and chemical transformations, as a characteristics of life.
Protoplasm also includes membranes, cytoplasmic contents and nucleus.
Protoplasm is “physical basis of life”.
Protoplasm is the medium & source of all biological activities.
Protoplasm basically differentiates a nonliving from living.
HISTORY :
Corti (1772) observed protoplasm first time.
Felix Dujardin (1835) studied the jelly-like substance in protozoa and called it sarcode. i.e. flesh of
cell.
J.E. Purkinje (1840) coined the term protoplasm for the living substance.
Hugo von Mohl (1846) applied this name (protoplasm) for the contents of the embryonic cells of the
plants.
Max Schultze (1863) stated that protoplasm is the physical basis of life.
Hanstein (1880) proposed the term protoplast for such organized mass of protoplasm, without cell
wall in plants.
O. Hertwig (1892) propound the protoplasmic theory according to which all living matter, out of which
animals and plants are formed, is protoplasm.
Fisher, Hardy and Wilson (1916) proposed colloidal theory of protoplasm.
PHYSICAL NATURE OF PROTOPLASM
Protoplasm is a greyish, translucent, jelly-like, odourless and viscous substance.
Protoplasm is heavier than water.
Protoplasm behaves as a moderate conductor of electricity.
Size of colloidal particles is 0.001 to 0.1 m.
Mineral ions and smaller inorganic and organic molecules (sugar, salts, simple acids, bases etc.)
occurs as crystalloid solutes in the protoplasm, while larger, organic molecules (proteins, polysac
charides and nucleic acid) occur as colloidal solutes. Thus protoplasm is crystallo-colloidal
mixture.
Scientists call it a “mixture of mixtures”, or “supermixture”.
Protoplasm is a reversible coloidal system i.e. it can change from a thicker, highly viscous “gel”
state to a comparatively more fluid and less viscous “sol” state and vice-versa.
Being a liquid mixture, the protoplasm has a surface tension.
Viscosity = 2 – 20 centipoises.
Refractive index = 1.4
Physical Appearance of Protoplasm :
Old theories : Protoplasm appears differently in different
phases.
Alveolar theory-Butschli (1892) : Protoplasm consists
of bubbles or alveoli of a fluid of lesser density distributed
in a fluid of greater density.
Granular theory : Altmann(1893) : The protoplasm
consists of numerous fine granules dispersed uniformly
in homogeneous fluid medium.
Fibriller theory-Fisher (1894) and Flemming (1897)
This theory maintains that protoplasm consists of
numerous minute fibrils or thread-like structures
dispersed in a fluid medium.
Page 2
RESONANCE KVPY_BIOMOLECULES-1 # 2
Reticular theory-Hanstein, Klein and Carnoy : According to this theory protoplasm consists of numerous
minute fibrils which forms a network or reticulum in a fluid medium.
MODERN COLLOIDAL THEORY :
This was first suggested by R.A. Fisher (1894) and latter by Hardy (1899) and Wilson (1916).
It consists of a fluid matrix or ground substance (liquid phase) dispersion phase and dispersed
phase of granules and globules.
The solid and semisolid particles range in diameter from 0.001 to 0.1 (1 or micron = 1/1000 mm.)
The particle are too big to form a suspension and are too small to form a true solution, they thus
remain in the matrix forming a colloidal system.
The liquid phase or dispersion phase of protoplasmic colloids consists mainly of water having dis
solved inorganic ions, salts and small molecules.
The dispersed phase comprises mainly of large molecules of proteins, lipids and carbohydrate.
Phase reversal in protoplasm is due to its colloidal nature. Non living colloid are irreversible in
phase change. (Gel Sol)
Protoplasm shows elasticity.
Elasticity, viscosity, contractility, rigidity are physical properties due to colloidal nature.
Protoplasm shows viscosity.
Colloidal particles show scattering of light, when a beam of light is passed through colloid it be comes
visible. It is called Tyndall effect.
Colloidal particles show zig-zag or irregular movement. The movements are called as Brownian
movement. It occurs during sol state.
Protoplasm responds to the stimulus of chemicals, light and heat or mechanical and thus it shows
irritability.
Protoplasm shows conductivity of impulse produced by stimulus.
All colloidal solution shows ageing. After some time (age) various activities stops.
MOVEMENTS OF PROTOPLASM
It can show following types of movement:
Amoeboid movement :
Naked mass of protoplasm shows creeping movement to form pseudopodia. e.g. Amoeba, Slime
moulds, Neutrophils.
Cyclosis :
Streaming movement of cytoplasm is called cyclosis. It is of two types.
(a) circulation (b) Rotation
CHEMICAL NATURE OF PROTOPLASM
Elements :
About 36 elements are known to occur in protoplasm.
About 13 elements are found in more quantity. These universal elements are C, H, O, N, Cl, Ca, P,Na, K,
S, Mg, I, Fe.
Carbon, hydrogen, nitrogen and oxygen are found greatly in the protoplasm and make up 95% of all living
material. Thus they are called major element.
Remaining 23 elements are called trace element. They are in very small amount (about 0.376%). they are
copper, Cobalt, magnese, zinc, chromium molybdenum, boron, silicon, vanadium, nickle, lflorine, selenium etc
Elements % amount
Oxygen 62
Carbon 20
Hydrogen 10
Nitrogen 3
Calcium 2.5
Phosphorus 1.14
Chlorine 0.16
Sulphur 0.14
Potassium 0.11
Sodium 0.10
Magnesium 0.07
Iron 0.01
Iodine 0.014
Element
Earth's crust Human body
Hydrogen (H) 0.14 0.5
Carbon (C) 0.03 18.5
Oxygen (O) 46.6 65.0
Nitrogen (N) Very little 3.3
Sulphur (S) 0.03 0.3
Sodium (Na) 2.8 0.2
Calcium (Ca) 3.6 1.5
Magnesium (Mg) 2.1 0.1
Silicon (Si) 27.7 negligible
% Weight of
A comparison of elements present in non-living and living matter
Page 50
RESONANCE Mole Concept-1 - 8
Step-3 To calculate the value of �n�
n = massformulaEmpirical
massMolecular
=
59
118
= 2
Step-4 To calculate the molecular formula of the salt.
Molecular formula = n × (Empirical formula) = 2 × C
2
H
3
O
2
= C
4
H
6
O
4
Thus the molecular formula is C
4
H
6
O
4.
DENSITY :
It is of two type.
Absolute density
Relative density
For Liquid and Solids
Absolute density =
volume
mass
Relative density or specific gravity = C4atwaterofdensity
cetansubstheofdensity
/
We know that density of water at 4ºC = 1 g/ml.
For Gases :
Absolute density (mass/volume) = volumeMolar
massMolar
Relative density or Vapour density :
Vapour density is defined as the density of the gas with respect to hydrogen gas at the same temperature
and pressure.
Vapour density =
2H
gas
d
d
V.D. =
2H
gas
M
M
=
2
Mgas
M
gas
= 2 V.D.
Relative density can be calculated w.r.t. to other gases also.
Example-11 What is the V.D. of SO
2
with respect to CH
4
Solution V.D. =
4
2
CH.W.M
SO.W.M
V.D =
16
64
= 4
Example-12 7.5 litre of the particular gas at S.T.P. weighs 16 gram. What is the V.D. of gas
Solution 7.5 litre = 16 gram
moles =
M
16
4.22
5.7
.
M = 48 gram V.D =
2
48
= 24
Page 51
RESONANCE Mole Concept-1 - 9
Chemical Reaction :
It is the process in which two or more than two substances interact with each other where old bonds are
broken and new bonds are formed.
Chemical Equation :
All chemical reaction are represented by chemical equations by using chemical formula of reactants and
products. Qualitatively a chemical equation simply describes what the reactants and products are. However,
a balanced chemical equation gives us a lot of quantitative information. Mainly the molar ratio in which
reactants combine and the molar ratio in which products are formed.
Attributes of a balanced chemical equation:
(a) It contains an equal number of atoms of each element on both sides of equation.(POAC)
(b) It should follow law of charge conservation on either side.
(c) Physical states of all the reagents should be included in brackets.
(d) All reagents should be written in their standard molecular forms (not as atoms )
(e) The coefficients give the relative molar ratios of each reagent.
Example-13 Write a balance chemical equation for following reaction :
When potassium chlorate (KClO
3
) is heated it gives potassium chloride (KCl) and oxygen (O
2
).
Solution KClO
3
(s) +,+0 KCl (s) + O2 (g) (unbalanced chemical equation )
2KClO
3
(s) +,+0 2 KCl (s) + 3 O2 (g) (balanced chemical equation)
Remember a balanced chemical equation is one which contains an equal number of atoms of each
element on both sides of equation.
Interpretation of balanced chemical equations :
Once we get a balanced chemical equation then we can interpret a chemical equation by following
ways
Mass - mass analysis
Mass - volume analysis
Mole - mole analysis
Vol - Vol analysis (separately discussed as eudiometry or gas analysis)
Now you can understand the above analysis by following example
Mass-mass analysis :
Consider the reaction
2KClO
3
+,+ 2KCl + 3O
2
According to stoichiometry of the reaction
mass-mass ratio: 2 × 122.5 : 2 × 74.5 : 3 × 32
or KClofMass
KClOofMass 3
=
5.742
5.1222
!
!
2
3
OofMass
KClOofMass
=
323
5.1222
!
!
Page 99
(a) the average velocity of the point during the time of motion;
;k=kk ds nkSjku d.k dk vkSlr osx
(b) the maximum velocity;
d.k dk vf/kdre osx
(c) the time t
0
at which the instantaneous velocity is equal to the mean velocity averaged over the first t
0
seconds.
vkjs[k esa og {k.k t
0
D;k gksxk tc rkR{kf.kd osx izFke t
0
lsd.M le; rd] ds vkSlr osx ds cjkcj gksxkA
Ans : (a) 10 cm/s; (b) 25 cm/s; (c) t
0
= 16s
Sol. the slope of displacement time graph gives velocity.
(a) Average velocity =
timetotal
ntdisplacemetotal
=
20
2
=
10
1
m/s = 10 cm/s
The given graph can be divided into three parts.
(i) OA This part of graph is increasing order graph. So, velocity increases from O to A and acceleration
is positive.
(ii) AB This part of graph is constant slope graph (straight line). It means velocity remains constant
during AB.
(b) BC This part of graph is decreasing order graph.
So, velocity decreases and acceleration is negative.
From this discussion, it is clear that during AB velocity is constant and maximum.
v
max
= slope of AB portion of graph
=
AD
BD
=
4
1
m/s = 25 cm/s.
(c) Instantaneous velocity is given by slope of a point on s-t graph.
Since, straight line OP is tangent at the point P in fig.
So, instantaneous velocity at point P is equal to average velocity between O to P. The corresponding times
is t
0
= 16 sec.
Sol. foLFkkiu≤ oØ d h <ky osx d s cjkcj gksrh gS
(a) vkSlr osx =
le;dqy
foLFkkiudqy
=
20
2
=
10
1
m/s = 10 cm/s
Page 100
A
O
0.4 D
10 14 16 20
C
P
B1.4
2.0
d
is
p
la
ce
m
e
n
t
(i
n
m
)
le; ls- ek=kd esa ( )
fo
LF
kki
u
e
k=
kd
e
sa
(
m
)
Time (in sec.)
fn;k x;k oØ rhu Hkkxkssa esa foHkkft r fd ;k t k ld rk gS
(i) OA oØ d k ;g Hkkx d h <+ky /kukRed o c<+rs Ø e esa gS] vr% O ls A rd osx c<+rk gS o Roj.k /kukRed gSA
(ii) AB oØ d k ;g Hkkx fu;r <ky gSA bld k vFkZ gS fd AB d s nkSjku osx fu;r gSA
(b) BC oØ d k ;g Hkkx d h <+ky ?kVrs Ø e esa gSA
vr% osx ?kV jgk gS rFkk Roj.k _ .kkRed gSA
blls ;g fl) gksrk gS fd Hkkx AB d s nkSjku osx vf/kd re rFkk fu;r gSA
v
max
= oØ d s AB Hkkx d h <ky
=
AD
BD
=
4
1
m/s = 25 cm/s.
(c) s-t oØ d s fd lh fcUnq ij rkR{kf.kd osx d k eku ml fcUnq ij oØ d h <ky d s cjkcj gSA
pwafd , lh/kh js[kk OP fcUnq P ij Li'kZ js[kk gSA
vr% fcUnq P ij rkR{kf.kd osx O ls P d s chp vkSlr osx d s leku gSA laxr le; t
0
= 16 sec gS
RESONANCE KVPY_BIOMOLECULES-1 # 1
BIOMOLECULES-1
INTRODUCTION :
Living matter of cell is called protoplasm.
Protoplasm (Gr. Protos-first+ Plasma-organization) is a living organized substance which is the place
for all physical and chemical transformations, as a characteristics of life.
Protoplasm also includes membranes, cytoplasmic contents and nucleus.
Protoplasm is “physical basis of life”.
Protoplasm is the medium & source of all biological activities.
Protoplasm basically differentiates a nonliving from living.
HISTORY :
Corti (1772) observed protoplasm first time.
Felix Dujardin (1835) studied the jelly-like substance in protozoa and called it sarcode. i.e. flesh of
cell.
J.E. Purkinje (1840) coined the term protoplasm for the living substance.
Hugo von Mohl (1846) applied this name (protoplasm) for the contents of the embryonic cells of the
plants.
Max Schultze (1863) stated that protoplasm is the physical basis of life.
Hanstein (1880) proposed the term protoplast for such organized mass of protoplasm, without cell
wall in plants.
O. Hertwig (1892) propound the protoplasmic theory according to which all living matter, out of which
animals and plants are formed, is protoplasm.
Fisher, Hardy and Wilson (1916) proposed colloidal theory of protoplasm.
PHYSICAL NATURE OF PROTOPLASM
Protoplasm is a greyish, translucent, jelly-like, odourless and viscous substance.
Protoplasm is heavier than water.
Protoplasm behaves as a moderate conductor of electricity.
Size of colloidal particles is 0.001 to 0.1 m.
Mineral ions and smaller inorganic and organic molecules (sugar, salts, simple acids, bases etc.)
occurs as crystalloid solutes in the protoplasm, while larger, organic molecules (proteins, polysac
charides and nucleic acid) occur as colloidal solutes. Thus protoplasm is crystallo-colloidal
mixture.
Scientists call it a “mixture of mixtures”, or “supermixture”.
Protoplasm is a reversible coloidal system i.e. it can change from a thicker, highly viscous “gel”
state to a comparatively more fluid and less viscous “sol” state and vice-versa.
Being a liquid mixture, the protoplasm has a surface tension.
Viscosity = 2 – 20 centipoises.
Refractive index = 1.4
Physical Appearance of Protoplasm :
Old theories : Protoplasm appears differently in different
phases.
Alveolar theory-Butschli (1892) : Protoplasm consists
of bubbles or alveoli of a fluid of lesser density distributed
in a fluid of greater density.
Granular theory : Altmann(1893) : The protoplasm
consists of numerous fine granules dispersed uniformly
in homogeneous fluid medium.
Fibriller theory-Fisher (1894) and Flemming (1897)
This theory maintains that protoplasm consists of
numerous minute fibrils or thread-like structures
dispersed in a fluid medium.
Page 2
RESONANCE KVPY_BIOMOLECULES-1 # 2
Reticular theory-Hanstein, Klein and Carnoy : According to this theory protoplasm consists of numerous
minute fibrils which forms a network or reticulum in a fluid medium.
MODERN COLLOIDAL THEORY :
This was first suggested by R.A. Fisher (1894) and latter by Hardy (1899) and Wilson (1916).
It consists of a fluid matrix or ground substance (liquid phase) dispersion phase and dispersed
phase of granules and globules.
The solid and semisolid particles range in diameter from 0.001 to 0.1 (1 or micron = 1/1000 mm.)
The particle are too big to form a suspension and are too small to form a true solution, they thus
remain in the matrix forming a colloidal system.
The liquid phase or dispersion phase of protoplasmic colloids consists mainly of water having dis
solved inorganic ions, salts and small molecules.
The dispersed phase comprises mainly of large molecules of proteins, lipids and carbohydrate.
Phase reversal in protoplasm is due to its colloidal nature. Non living colloid are irreversible in
phase change. (Gel Sol)
Protoplasm shows elasticity.
Elasticity, viscosity, contractility, rigidity are physical properties due to colloidal nature.
Protoplasm shows viscosity.
Colloidal particles show scattering of light, when a beam of light is passed through colloid it be comes
visible. It is called Tyndall effect.
Colloidal particles show zig-zag or irregular movement. The movements are called as Brownian
movement. It occurs during sol state.
Protoplasm responds to the stimulus of chemicals, light and heat or mechanical and thus it shows
irritability.
Protoplasm shows conductivity of impulse produced by stimulus.
All colloidal solution shows ageing. After some time (age) various activities stops.
MOVEMENTS OF PROTOPLASM
It can show following types of movement:
Amoeboid movement :
Naked mass of protoplasm shows creeping movement to form pseudopodia. e.g. Amoeba, Slime
moulds, Neutrophils.
Cyclosis :
Streaming movement of cytoplasm is called cyclosis. It is of two types.
(a) circulation (b) Rotation
CHEMICAL NATURE OF PROTOPLASM
Elements :
About 36 elements are known to occur in protoplasm.
About 13 elements are found in more quantity. These universal elements are C, H, O, N, Cl, Ca, P,Na, K,
S, Mg, I, Fe.
Carbon, hydrogen, nitrogen and oxygen are found greatly in the protoplasm and make up 95% of all living
material. Thus they are called major element.
Remaining 23 elements are called trace element. They are in very small amount (about 0.376%). they are
copper, Cobalt, magnese, zinc, chromium molybdenum, boron, silicon, vanadium, nickle, lflorine, selenium etc
Elements % amount
Oxygen 62
Carbon 20
Hydrogen 10
Nitrogen 3
Calcium 2.5
Phosphorus 1.14
Chlorine 0.16
Sulphur 0.14
Potassium 0.11
Sodium 0.10
Magnesium 0.07
Iron 0.01
Iodine 0.014
Element
Earth's crust Human body
Hydrogen (H) 0.14 0.5
Carbon (C) 0.03 18.5
Oxygen (O) 46.6 65.0
Nitrogen (N) Very little 3.3
Sulphur (S) 0.03 0.3
Sodium (Na) 2.8 0.2
Calcium (Ca) 3.6 1.5
Magnesium (Mg) 2.1 0.1
Silicon (Si) 27.7 negligible
% Weight of
A comparison of elements present in non-living and living matter
Page 50
RESONANCE Mole Concept-1 - 8
Step-3 To calculate the value of �n�
n = massformulaEmpirical
massMolecular
=
59
118
= 2
Step-4 To calculate the molecular formula of the salt.
Molecular formula = n × (Empirical formula) = 2 × C
2
H
3
O
2
= C
4
H
6
O
4
Thus the molecular formula is C
4
H
6
O
4.
DENSITY :
It is of two type.
Absolute density
Relative density
For Liquid and Solids
Absolute density =
volume
mass
Relative density or specific gravity = C4atwaterofdensity
cetansubstheofdensity
/
We know that density of water at 4ºC = 1 g/ml.
For Gases :
Absolute density (mass/volume) = volumeMolar
massMolar
Relative density or Vapour density :
Vapour density is defined as the density of the gas with respect to hydrogen gas at the same temperature
and pressure.
Vapour density =
2H
gas
d
d
V.D. =
2H
gas
M
M
=
2
Mgas
M
gas
= 2 V.D.
Relative density can be calculated w.r.t. to other gases also.
Example-11 What is the V.D. of SO
2
with respect to CH
4
Solution V.D. =
4
2
CH.W.M
SO.W.M
V.D =
16
64
= 4
Example-12 7.5 litre of the particular gas at S.T.P. weighs 16 gram. What is the V.D. of gas
Solution 7.5 litre = 16 gram
moles =
M
16
4.22
5.7
.
M = 48 gram V.D =
2
48
= 24
Page 51
RESONANCE Mole Concept-1 - 9
Chemical Reaction :
It is the process in which two or more than two substances interact with each other where old bonds are
broken and new bonds are formed.
Chemical Equation :
All chemical reaction are represented by chemical equations by using chemical formula of reactants and
products. Qualitatively a chemical equation simply describes what the reactants and products are. However,
a balanced chemical equation gives us a lot of quantitative information. Mainly the molar ratio in which
reactants combine and the molar ratio in which products are formed.
Attributes of a balanced chemical equation:
(a) It contains an equal number of atoms of each element on both sides of equation.(POAC)
(b) It should follow law of charge conservation on either side.
(c) Physical states of all the reagents should be included in brackets.
(d) All reagents should be written in their standard molecular forms (not as atoms )
(e) The coefficients give the relative molar ratios of each reagent.
Example-13 Write a balance chemical equation for following reaction :
When potassium chlorate (KClO
3
) is heated it gives potassium chloride (KCl) and oxygen (O
2
).
Solution KClO
3
(s) +,+0 KCl (s) + O2 (g) (unbalanced chemical equation )
2KClO
3
(s) +,+0 2 KCl (s) + 3 O2 (g) (balanced chemical equation)
Remember a balanced chemical equation is one which contains an equal number of atoms of each
element on both sides of equation.
Interpretation of balanced chemical equations :
Once we get a balanced chemical equation then we can interpret a chemical equation by following
ways
Mass - mass analysis
Mass - volume analysis
Mole - mole analysis
Vol - Vol analysis (separately discussed as eudiometry or gas analysis)
Now you can understand the above analysis by following example
Mass-mass analysis :
Consider the reaction
2KClO
3
+,+ 2KCl + 3O
2
According to stoichiometry of the reaction
mass-mass ratio: 2 × 122.5 : 2 × 74.5 : 3 × 32
or KClofMass
KClOofMass 3
=
5.742
5.1222
!
!
2
3
OofMass
KClOofMass
=
323
5.1222
!
!
Page 99
(a) the average velocity of the point during the time of motion;
;k=kk ds nkSjku d.k dk vkSlr osx
(b) the maximum velocity;
d.k dk vf/kdre osx
(c) the time t
0
at which the instantaneous velocity is equal to the mean velocity averaged over the first t
0
seconds.
vkjs[k esa og {k.k t
0
D;k gksxk tc rkR{kf.kd osx izFke t
0
lsd.M le; rd] ds vkSlr osx ds cjkcj gksxkA
Ans : (a) 10 cm/s; (b) 25 cm/s; (c) t
0
= 16s
Sol. the slope of displacement time graph gives velocity.
(a) Average velocity =
timetotal
ntdisplacemetotal
=
20
2
=
10
1
m/s = 10 cm/s
The given graph can be divided into three parts.
(i) OA This part of graph is increasing order graph. So, velocity increases from O to A and acceleration
is positive.
(ii) AB This part of graph is constant slope graph (straight line). It means velocity remains constant
during AB.
(b) BC This part of graph is decreasing order graph.
So, velocity decreases and acceleration is negative.
From this discussion, it is clear that during AB velocity is constant and maximum.
v
max
= slope of AB portion of graph
=
AD
BD
=
4
1
m/s = 25 cm/s.
(c) Instantaneous velocity is given by slope of a point on s-t graph.
Since, straight line OP is tangent at the point P in fig.
So, instantaneous velocity at point P is equal to average velocity between O to P. The corresponding times
is t
0
= 16 sec.
Sol. foLFkkiu≤ oØ d h <ky osx d s cjkcj gksrh gS
(a) vkSlr osx =
le;dqy
foLFkkiudqy
=
20
2
=
10
1
m/s = 10 cm/s
Page 100
A
O
0.4 D
10 14 16 20
C
P
B1.4
2.0
d
is
p
la
ce
m
e
n
t
(i
n
m
)
le; ls- ek=kd esa ( )
fo
LF
kki
u
e
k=
kd
e
sa
(
m
)
Time (in sec.)
fn;k x;k oØ rhu Hkkxkssa esa foHkkft r fd ;k t k ld rk gS
(i) OA oØ d k ;g Hkkx d h <+ky /kukRed o c<+rs Ø e esa gS] vr% O ls A rd osx c<+rk gS o Roj.k /kukRed gSA
(ii) AB oØ d k ;g Hkkx fu;r <ky gSA bld k vFkZ gS fd AB d s nkSjku osx fu;r gSA
(b) BC oØ d k ;g Hkkx d h <+ky ?kVrs Ø e esa gSA
vr% osx ?kV jgk gS rFkk Roj.k _ .kkRed gSA
blls ;g fl) gksrk gS fd Hkkx AB d s nkSjku osx vf/kd re rFkk fu;r gSA
v
max
= oØ d s AB Hkkx d h <ky
=
AD
BD
=
4
1
m/s = 25 cm/s.
(c) s-t oØ d s fd lh fcUnq ij rkR{kf.kd osx d k eku ml fcUnq ij oØ d h <ky d s cjkcj gSA
pwafd , lh/kh js[kk OP fcUnq P ij Li'kZ js[kk gSA
vr% fcUnq P ij rkR{kf.kd osx O ls P d s chp vkSlr osx d s leku gSA laxr le; t
0
= 16 sec gS
