Gravitation
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Two Concentric Spherical Shells of Uniform Density And Having Masses \( M_1 \) and \( M_2 \) Are Situated As Shown In The Figure. Find The Force On A Particle Of Mass m, When The Particle Is Located At (i)r=a, (ii)r=b, and (iii)r=c. The Distance r Is Measured From The Centre Of The Shells.
Two concentric spherical shells of masses and have uniform density . These two spherical shells behave as if their masses and are concentrated at their common centre. (i) At the…
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A Uniform Solid Sphere Of Mass “M” And Radius “a” Is Cut Into Two Equal Halves By A Diametrical Plane. Calculate The Gravitational Attraction Between The Two Halves.
Let us consider a solid sphere of mass “M” and radius “a” and a strip of thickness dx at a distance x from the centre o of the sphere. The…
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A Straight Frictionless Tunnel Is Bored Through The Earth From One Point Of Its Surface To Another Point. Show That The Object In The Tunnel Will Execute Simple Harmonic Motion. Calculate The Time Period.
Motion of an object in the tunnel through the earth from one point to another point of the surface: Let us consider the earth is a sphere of radius ,…
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A Straight Frictionless Tunnel Is Bored Through The Earth Along A Diameter. A Body Is Dropped At One End. Show That It Execute A Simple Harmonic Motion. Find The Expression For The Time Period.
Motion of a body in a tunnel through the earth along a diameter: Let us consider the mass of the earth is and the radius is with centre at the…
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Calculate Gravitational Self Energy Of A Uniform Sphere Of Mass “M” And Radius “R”.
Gravitational self energy: Let us consider a uniform sphere of radius , mass and the density of the material of the sphere is . Let us consider the uniform sphere…
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Suppose The Earth Contracts Suddenly To Half Its Present Radius. What Would Be The Duration Of A Day?
Let us consider the mass and the radius of the earth is and respectively. When the radii are and , the moment of inertia of the earth are and respectively,…
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Calculate The Height Of An Artificial Satellite.
Height of an artificial satellite: Let us consider an artificial satellite revolves around the earth with a velocity , at a height from the surface of the earth. Mass of…
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What Is Geo-Stationary Satellite? Calculate The Altitude Of Geo-Stationary Satellite.
Geo-stationary satellite: When a satellite revolves around the earth at a suitable height from the surface of the earth, with the same velocity in the same direction as the earth…