Questions
A uniform ring of mass m is lying at a distance a form the centre of a sphere of mass M just over the sphere (where a is the radius of the ring as well as that of the sphere). Then magnitude of gravitational force between them is
detailed solution
Correct option is D
For a small mass dm, distance from the center of sphere is 2a. force along ‘dm’ G,M,dm4a2=FComponent of force F sin get cancelled net force 2Fcos θ . For the entire ring- GM4a2m2×2cosθGMm4a23a2a=3GMm8a2Alternative solution:-field intensity due the ring at the centre of the sphere is g=GMx(R2+x2)32=GMa(a2+3a2)32=3GM8a2 F=mg=3GMm8a2Similar Questions
A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolly is displaced from its equilibrium position by a distance x and released. The trolly executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)
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