A set is a well-defined collection of objects, whose elements are fixed and cannot vary. It means set doesn’t change from person to person. Like for example, the set of natural numbers up to 7 will remain the same as {1,2,3,4,5,6,7}. Still, if we say the set of best players in a football team, then the name of footballers could vary every time we ask about the best players, as each person has its own choice to consider the best player. Similarly, if we speak about the set of rivers in India, the elements of the set will remain the same. So, this is a real-life example of a set. In mathematics, we represent the sets in curly brackets { }.

Relation between linear velocity and angular velocity

Let us consider the randomly shaped body undergoing a rotational motion as shown in the figure below. The linear velocity of the particle is related to the angular velocity. While considering the rotational motion of a rigid body on a fixed axis, the extended body is considered as a system of particles moving in a circle lying on a plane that is perpendicular to the axis, such as the center of rotation lies on the axis.

In this figure, the particle P has been shown to rotate over a fixed axis passing through O. Here, the particle represents a circle on the axis. The radius of the circle is the perpendicular distance between point P and the axis. The angle indicates the angular displacement Δθ of the given particle at time Δt. The average angular velocity in the time Δt is Δθ/Δt. Since Δt tends to zero, the ratio Δθ/Δt reaches a limit which is known as the instantaneous angular velocity dθ/dt. The instantaneous angular velocity is denoted by ω.

From the knowledge of circular motion, we can say that the magnitude of the linear velocity of a particle traveling in a circle relates to the angular velocity of the particle ω by the relation υ/ω= r, where r denotes the radius. At any instant, the relation v/ r = ω applies to every particle that has a rigid body.

If the perpendicular distance of a particle from a fixed axis is r_i, the linear velocity at a given instant v is given by the relation,

V_i = ωr_i

Similarly, we can write the expression for the linear velocity for n different particles comprising the system. From the expression, we can say that for particles lying on the axis, the tangential velocity is zero as the radius is zero. Also, the angular velocity ω is a vector quantity which is constant for all the particles comprising the motion.

Let us consider the randomly shaped body undergoing a rotational motion as shown in the figure below. The linear velocity of the particle is related to the angular velocity. While considering the rotational motion of a rigid body on a fixed axis, the extended body is considered as a system of particles moving in a circle lying on a plane that is perpendicular to the axis, such as the center of rotation lies on the axis.

In this figure, the particle P has been shown to rotate over a fixed axis passing through O. Here, the particle represents a circle on the axis. The radius of the circle is the perpendicular distance between point P and the axis. The angle indicates the angular displacement Δθ of the given particle at time Δt. The average angular velocity in the time Δt is Δθ/Δt. Since Δt tends to zero, the ratio Δθ/Δt reaches a limit which is known as the instantaneous angular velocity dθ/dt. The instantaneous angular velocity is denoted by ω.

From the knowledge of circular motion, we can say that the magnitude of the linear velocity of a particle traveling in a circle relates to the angular velocity of the particle ω by the relation υ/ω= r, where r denotes the radius. At any instant, the relation v/ r = ω applies to every particle that has a rigid body.

If the perpendicular distance of a particle from a fixed axis is r_i, the linear velocity at a given instant v is given by the relation,

V_i = ωr_i

Similarly, we can write the expression for the linear velocity for n different particles comprising the system. From the expression, we can say that for particles lying on the axis, the tangential velocity is zero as the radius is zero. Also, the angular velocity ω is a vector quantity which is constant for all the particles comprising the motion.

CCl₄ molecule has zero dipole moment although the c-cl bond are polar this is because the shape of the molecule is tetrahedral and this make it very symmetrical and the four polar bond cancel out each other. so they have zero dipole moment.

Be has electronic configuration 1S²,2S² and s orbital is completely filled and doesn't require any electron to complete its orbital.Hence, Be₂ doesn't exist at all.

According to Fajans rule....

The charge on the ion increases the covalent character also increases because.

a high charge containing cation can polarise the anion more easily

as in fecl3 the charge of fe is +3 and the charge of fe in FeCl₂ is +2

the charge of fe in FeCl₃ is more so fecl3 is more covalent

The presence of -OH group helps in formation of hydrogen bonding. This helps in solubility of ethanol in water.

Once an organ donor's family gives its consent and the organs are matched to a recipient, medical professionals are faced with the onerous challenge of transporting organs while ensuring that the harvested organ reaches its destination in the shortest possible time. This is done in order to preserve the harvested organs and involves the police and especially the traffic police department.

Services : Services are all those economic activities that are intangible and imply an interaction to be realised between service provider and consumer.

There are two types of issues, one where company and Lead Merchant Banker fix a price (called fixed price) and other, where the company and the Lead Manager (LM) stipulate a floor price or a price band and leave it to market forces to determine the final price (price discovery through book building process). Nowadays, all issues are normally done through the book built route. However, the fixed price route has been kept open to allow small and medium enterprises to offer shares on the SME platform of the exchanges.

Khelo India Programme is a national yojana/scheme for the development of sports in India. It was launched in the year 2018 by the then Sports Minister Col. Rajyavardhan Singh Rathore in Delhi. This program has been launched to improve the sports culture in India.

Aimed at mainstreaming sports as a tool for national development, economic development, community development and individual development, the Union Cabinet approved the execution of the revamped ‘Khelo India’ program by consolidating the ‘Rajiv Gandhi Khel Abhiyan’ (formerly called the ‘Yuva Krida & Khel Abhiyan’), the ‘Urban Sports Infrastructure Scheme’ and the National Sports Talent Search System Programme’. The program strives to promote “Sports for Excellence” as well as “Sports for All”.

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नहरों द्वारा खानों से कोयले और लोहे जैसे भारी पदार्थों को कारखानों तक ले जाना काफी सरल हो गया है।
नहरों द्वारा माल का आयात व निर्यात सबसे सस्ता पड़ता था।
बड़े-बड़े नगरों को जब इन नहरों से मिला दिया गया तो शहरवासियों को सस्ते परिवहन भी उपलब्ध हुए।
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