Answer :

The force exerted by the particle on the sphere is


The distance travelled is


Given


The mass of the particle is given as m, fixed on a sphere of radius R, where the particle makes a radius with an angle of 300 with vertical.


Formula Used


Using the conservation of static and dynamic energy such as potential and centripetal energy, we have the conservation equation as



where


m is the mass of the object, v is the velocity, R is the radius of the circular path, r is the radius of the object, h is the height.


Explanation


(a) The mass of the particle when horizontal is given as




Hence, force exerted by the sphere is.


(b) The distance travelled by the particle in terms of radian/degree is calculated as


The change in potential energy due to the angle of is



Equating the kinetic and potential energy together we get the value of velocity as



And



The equation formed is







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