Let the weight of the particle on the surface of the earth,
\(w=120=\cfrac { GMm }{ { R }^{ 2 } } \)
where, R = 6400 km = 6.4 X 10⁶ m
Hence, 120=\(\cfrac { GMm }{ \left( 6.4\times { 10 }^{ 6 } \right) ^{ 2 } } \)
Let the height h above the earth's surface, where its weight will be 30 N.
Hence,\(30=\cfrac { GMm }{ \left( h+R \right) ^{ 2 } } \)
\(30=\cfrac { GMm }{ \left( h+6.4\times 10^{ 6 } \right) ^{ 2 } } \)                         ...(ii)
On dividing Eq. (i) by Eq. (ii), we get
\(\cfrac { 120 }{ 30 } =\cfrac { GMm }{ \left( 6.4\times 10^{ 6 } \right) } \times \cfrac { \left( h+6.4\times { 10 }^{ 6 } \right) ^{ 2 } }{ GMm } \)
\(\cfrac { 4 }{ 1 } =\cfrac { \left( h+R \right) ^{ 2 } }{ { R }^{ 2 } } \Rightarrow 2=\cfrac { h+R }{ R } \)
\(\Rightarrow\) 2R = h + R
\(\Rightarrow\) h = 2R - R = R = 6400 km
= 6.4 x 10⁶m

Fertilizers are commercially produced plant nutrients. They supply nitrogen, phosphorus and potassium. They are used to ensure good vegetative growth, giving rise to healthy plants.
The two examples of fertilizers are:
1. Urea
2. Superphosphate (NPK)
Different between Fertilizer and Manure:

Solutions.When two reacting substances are kept in contact, the reaction does not take place or is very slow. But when their solutions are mixed, the reaction takes place very fast. This happens because in solutions, reacting substances come in contact with each other at molecular level. When solid washing soda is poured over cloths, it does not wash but when clothes are mixed with solution of washing soda, clothes are easily cleaned.
Colloids Some insoluble substances particularly in pharmaceuticals become effective when administered in colloidal form. many medicines are insoluble in water but are used in the form of colloids.
Suspensions. Many substances insoluble or sparingly soluble in dispersing medium become useful for analytical purpose when dispersed temporarily. For example, sparingly soluble barium sulphate dispersed in water is an opaque medium and is used for diagnostic X-rays.

(i) Most agriculture in INDIA is rain-fed. The success of crops in most areas is dependent on timely monsoons and sufficient rainfall spread through most of the growing seasons. Untimely rainfall spoils the crop and crop yield.
(ii) Since weather conditions such as drought and flood situation are unpredictable, varieties that can be grown in diverse climatic conditions are useful.

The wave velocity is the distance travelled by a wave per unit time. It remains constant in a given medium \(\left( v=v\lambda \right) \) . The particle velocity continuously changes with time. It is maximum at the mean position and zero at the extreme position.

Zero, because displacement of the rock is zero.

Here, M_e = 6 x 10²⁴ kg. M_s = 2 x 10³⁰, r = 1.5 x 10¹¹ m
\(F=G\frac { { m }_{ e }{ m }_{ s } }{ { r }^{ 2 } } \) = \(\frac { 6.67\times { 10 }^{ -11 }\times 6\times { 10 }^{ 24 }\times 6\times { 10 }^{ 30 } }{ { \left( 1.5\times { 10 }^{ 11 } \right) }^{ 2 } } N\)
 \(\frac { 6.67\times 12\times { 10 }^{ 21 } }{ 1.5\times 1.5 } =3.56\times { 10 }^{ 22 }N\) 

First law of motion as a special case of second law. According to second law,
 \(F= ma = m \left(\frac{u-v}{t}\right)\)
\(Ft = m \left(u-v\right)\) 
That is when F = 0, v = u for whatever time t is taken because \(m \neq 0.\) This means that the object will continue moving with uniform velocity u throughout the time t. If u is zero then v will also be zero. That is the object will remain at rest. This is nothing but Newton's first law of motion. Hence first law of motion is contained in the second law.

Here,u = 0,s = 10m,a = 5 \(m/s^{ 2 }\) 
\(\therefore v^{ 2 }-u^{ 2 }=2as\) 
\(\therefore v^{ 2 }-0^{ 2 }=2x5x10=100\) 
or \(v=\sqrt { 100 } \) =10 m/s
\(\therefore \) Distance travelled by the object = 125 m.

Characteristic is a particular from or a particular function. For example, generally human being has five finger in each hand. Thus, presence of five finger in each hand is a characteristic. Similarly, animals can run but trees like banyan tree cannot run, is also a characteristic.

An atom is the smallest particle of an element which may or may not have independent existence.On the other hand,'molecule' is the smallest particle of the element or compound which is capable of independent existence.For example helium (He) is an atom and can exist as such, whereas hydrogen atom cannot exist as such but exists as a molecule, i.e H₂ .A molecule may be made up of similar atoms or dissimilar atoms.

Decantation is the process of separating of insoluble solids from liquids. A suspension of solid particles in a liquid is allowed to stand for some time.Insoluble solid particle settle of solid down at the bottom due to their weight. This is called sedimentation. The clear liquid is then transferred into another container, without disturbing the settled. In other words, clear liquid is decanted and separated from solid.

Plants and Animals differ as given in the table below:

Height of object A,\({ h }_{ 1 }=\cfrac { 1 }{ 2 } g{ t }_{ 1 }^{ 2 }\)
Height of object B,\({ h }_{ 2 }=\cfrac { 1 }{ 2 } g{ t }_{ 2 }^{ 2 }\)
\(\therefore \) \({ h }_{ 1 }{ h }_{ 2 }={ t }_{ 1 }^{ 2 }:{ t }_{ 2 }^{ 2 }\)
or  \({ t }_{ 1 }:{ { t }_{ 2 }=\sqrt { { h }_{ 1 } } :\sqrt { { h }_{ 2 } } }\)
(i) Acceleration due to gravity is independent of mass of falling body. So, ratio remains the same
(ii) If bodies are hollow, then also ratio remains the  same, i.e.\({ t }_{ 1 }:{ { t }_{ 2 }=\sqrt { { h }_{ 1 } } :\sqrt { { h }_{ 2 } } }\)
 

(a) Gravitational force acting on the 50 kg,
mg= 50x 9.8 = 490N 
(b) Gravitational force acting on the 50 kg mass due to jupiter,
\({ F }_{ jupiter }=\cfrac { G\times { M }_{ jupiter }\times { { M }_{ person } } }{ \left( distance\quad of\quad jupiter\quad from\quad the\quad earth \right) ^{ 2 } } \)
\({ F }_{ jupiter }=\cfrac { 6.67\times { 10 }^{ -11 }\times 2\times { 10 }^{ 27 }\times 50 }{ 6.3\times { 10 }^{ 11 }\times 6.3\times { 10 }^{ 11 } } \)
\({ F }_{ jupiter }=\cfrac { 6.67\times 2\times 50\times { 10 }^{ -11+27-22 } }{ 6.3\times 6.3 } \)
F_Jupiter = 1.68 X 10^-5 N
\({ F }_{ saturn }=\cfrac { G\times M_{ saturn }\times { M }_{ person } }{ \left( distance\quad of\quad saturn\quad from\quad the\quad earth \right) ^{ 2 } } \)
\({ F }_{ saturn }=\cfrac { 6.67\times { 1 }0^{ -11 }\times 6\times { 10 }^{ 26 }\times 50 }{ 1.28\times 10^{ 12 }\times 1.28\times 10^{ 12 } } \)
\({ F }_{ saturn }=\cfrac { 6.67\times 6\times 50 }{ 1.28\times 1.28 } \times { 10 }^{ -11+26-24 }\)
F_saturn = 0.12x 10^-5N
\(\therefore\) Total gravitational force due to the jupiter and the saturn = (1.68x 10^-5+0.12x 10^-5)N
= 1.8x 10^-5 N
Thus, the combined force due to the planets jupiter and saturn (1.8 x10^-5) N is negligible as compared to the gravitational force due to the earth.
(ii) We know that, g at equator is less than g at poles (Antarctica). Thus, weight at equator is less than weight at pole (Antarctica). A bag of sugar weighs w at a certain place on the equator. If this bag is taken to Antarctica, then it will weigh more due to greater value of g.