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At noon, the sun and earth pull the objects on the earth’s surface in opposite directions. At midnight, the sun and the earth’s pull these objects in same direction. Is the weight of an objects, as measured by a spring balance on the earth’s surface, more at midnight as compared to its weight at noon?
The gravitational potential energy of a two-particle system is derived in this chapter as . Does it fallow from this equation that the potential energy for r = ∞ must be zero? Can we choose the potential energy for r = ∞ to be 20 J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?
The weight of a body at the poles is greater than the weight at the equator. Is it the actual weight or the apparent weight we are talking about? Does your answer depend on whether only the earth’s rotation is taken into account or the flattering of the earth’s at the poles is also taken into account?
The acceleration of moon with respect to earth is 0.0027ms-2and the acceleration of an apple falling on the earth surface is about 10ms-2. Assume that the radius of the moon is one fourth of the earth’s radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon towards the earth will be
Suppose the acceleration due to gravity at the earth’s surface is 10 ms-2 and at the surface of Mars it is4.0 ms-2. A 60 Kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in sky. Which part of figure (11-Q1) best represents the weight (net gravitational force) of the passenger as a function of time?
A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure (11-E1). A particle of mass m’ is placed on the line joining the two centers at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational on this particle due to the sphere and the shell if (a) r < x < 2r, (b) 2r < x < 2R. and (C) x > 2R.
A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in figure (11-E3). The point A is the Centre of the plane section of the first part and B is the Centre of the place section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.
Two small bodies of masses 2.00 kg and 4.00 Kg are kept at rest at a separation of 2.0 m. Where a particle of mass 0.10 kg should be placed to experience no net gravitational force from these bodies? The particle is placed at this point. What is the gravitational potential energy of the system of three particles with usual reference level?
The gravitational field in a region is given by
(a)Find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin.
(b)Find the potential at the points (12m,0) and (0, 5m) if the potential at the origin is taken to be zero.
(c) Find the change in gravitational Potential energy if a particle of mass 2 kg is taken from the origin to the point (12m, 5m).
(d)Find the change in potential energy If the particle is taken from (12m, 0) to (0,5m).
The gravitational field in a region is given by V= 20N Kg-1 (x+y).
(a) Show that the equation is dimensionally correct.
(b) Find the gravitational field at the point (x, y). Leave your answer in terms of the unit vectors i, j, k
(c) Calculate the magnitude of the gravitational force on a particle of mass 500g placed at the origin.
A pendulum having a bob of mass m is happening in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0.
(a) Find the speed of the ship due to rotation of the earth about its axis.
(b) Find the difference between T0 and the earth’s attraction on the bob.
(c) If the ship sails at speed . what is the tension in the string? Angular speed of earth’s rotation is ω and radius of the earth is R.