Text Solution
Solution : Weight of a body of mass m on the earth.s surface , `W =mg=(GMm)/(R^2)` where M and R are the mass and the radius of the earth. <br> when mass remains constant and radius doubles, then weight `W_1=(GMm)/((2R)^2)=(GMm)/(4R^2)` <br> `therefore (W_1)/W=(GMm)/(4R^2)*(R^2)/(GMm) =1/4` <br> Hence, new weight would be `1/4` th of the present weight.
1. Gravitation:
(i) Every object in this universe attract other objects with some force, which depends on the masses of the objects and distance between them. This force is called as force of gravitation.
(ii) Newton's Universal Law of Gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. It can be formulated as F=Gm1m2d2.
(iii) Gravitational Constant G is equal to the force of attraction between two unit point masses, when they are separated by a unit distance, as measured from their centres. Its value in SI units is 6.67×10-11 N m2 kg-2.
(iv) Force of gravity is a special case of the force of gravitation when one among the two bodies has infinitely large mass as compared to the other body.
(v) The phenomena like (a) the motion of the moon around the earth, (b) the motion of planets around the Sun and the occurance of high tide and low tide can be explained by the law of gravitation.
2. Free Fall:
(i) Whenever objects fall towards the earth under gravitational force alone, we say that the objects are in free fall.
(ii) Acceleration due to gravity is the acceleration with which a body falls freely towards any heavenly body such as Earth. It is formulated as g=GMeRe2. Its mean value on Earth is 9.81 m s-2. (G,Me and Re are Universal Gravitational constant, Mass of the Earth and Radius of the Earth)
(iii) Acceleration due to gravity is maximum at poles. Its value decreases towards the equator, high up in the mountains, deep inside the earth and in space. Its value is zero at the centre of the Earth.
3. Mass and Weight:
(i) Mass is the amount of matter contained in a body. It is a scalar quantity, and its SI unit is kilogram (kg).
(ii) Weight is the pull exerted on a body by the Earth. It is defined as the product of mass m and acceleration due to gravity g It is a vector quantity, and its SI unit is the newton.
(iii) The mass of an object is constant and does not change from place to place whereas its weight depends on its location because g depends on location.
(iv) The acceleration due to gravity on the moon is one-sixth of that on Earth.
(v) Equations of motion for a freely falling body are
(a) v=u+gt
(b) h=ut+12gt2
(c) v2-u2=2gh
Where ' u' is the initial velocity, ‘v’ is the final velocity; 'g' is the acceleration due to gravity; 'h' is the height and 't' is the time in seconds.
4. Thrust and Pressure:
(i) A force on a body perpendicular to its surface is known as thrust. SI unit of thrust is newton ( N).
(ii) The thrust F acting on a unit area A of a surface is called pressure P. It is formulated as P=FA.
(iii) The SI unit of pressure is 'pascal' (Pa). It is defined as a force of 1 N acting perpendicularly on an area of 1 m2.
(iv) The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area. This is the reason why a nail has a pointed tip, knives have sharp edges and buildings have wide foundations.
5. Archimedes Principle:
(i) The upward force experienced by a body when partly or fully immersed in a fluid is called upthrust or buoyant force, whereas the phenomenon responsible for this force is called buoyancy.
(ii) When the upthrust acting in on a body (in a liquid) is less than the weight of the body, it sinks.
(iii) When the upthrust acting in on a body (in a liquid) is greater than the weight of the body, it floats.
(iv) Archimedes' Principle states that when a body is partially or wholly immersed in a fluid, it experiences an upthrust (or apparently loses its weight), which is equal to the weight of the fluid displaced by the immersed part of the body.
6. Relative Density:
(i) Mass per unit volume of a body is called density. SI unit of density is kg m-3.
(ii) The ratio between the density of a substance and density of water is known as the relative density of the substance. Relative Density=Density of a substance Density of Water
(iii) The relative density of a body has no units.
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