Gravitation and Pressure
Synopsis
- Gravitation: The gravitational force of the earth is responsible for holding the atmosphere above the earth and it also keeps us firmly on the ground.
- Universal Law of Gravitation: Everybody in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The direction offeree is along the line joining the centres of the two bodies.
- Free Fall: The falling of a body from a height towards the earth under the gravitational force of earth (with no other forces acting on it) is called a free fall.
Motion of bodies under the influence of gravitational force of the earth. Since, the freely falling bodies fall with uniformly accelerated motion, the three equations of motion derived earlier for bodies under uniform acceleration can be applied to the motion of freely falling bodies.
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General equations of motion
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Equations of motion for freely falling bodies
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\[v=u+at\]
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Changes to
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\[V=u\pm gt\]
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\[S=ut+\frac{1}{2}a{{t}^{2}}\]
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Changes to
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\[h=ut\pm \frac{1}{2}g{{t}^{2}}\]
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\[{{v}^{2}}-{{u}^{2}}=2as\]
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Changes to
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\[{{v}^{2}}-{{u}^{2}}=\pm 2gh\]
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- Mass (m): It is one of the fundamental property of the body. The mass of the body is the quantity of matter contained in it. The mass of the body is constant and does not change from place to place. The mass of a body cannot be zero.
- Weight: The weight of a body is the force with which it is attracted towards the centre of the earth.
- Thrust: Thrust is defined as the force acting on a body normal (perpendicular) to its surface.
- Up thrust or buoyant force: When a body is immersed in a fluid completely or partly, the oody experiences an upward force by the fluid. This upward force exerted by the fluid on the immersed body is known as'upthrust7 or 'buoyant force'. The property of a fluid to exert buoyant force on an object immersed in it is known as'buoyancy7.
- Archimedes' Principle: When a body is partially or completely immersed in a fluid at rest, it experiences an up thrust which is equal to the weight of the fluid displaced by it.
Due to the up thrust acting on the body, the body apparently loses a part of its weight and the apparent loss of weight is equal to the up thrust.
Thus, for a body either partially or completely immersed in a fluid, up thrust = weight of the fluid displaced =apparent loss of weight of the body.
- Relative density of a substance is defined as the ratio of density of the substance to the density of water at \[{{4}^{{}^\circ }}C\]
