A hemisphere of mass M and radius R rests on a smooth horizontal table. A vertical rod of mass m is held between two smooth guide walls supported on the sphere as shown. There is no friction between the rod and the sphere. A horizontal string tied to the sphere keeps the system at rest.

(a) Find tension in the string.
(b) Find the acceleration of the hemisphere immediately after the string is cut.

Two equal spheres of mass m are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and reduces to rest. Then:

A sphere of mass M is held at rest on a horizontal floor. One end of a light string is fixed at a point that is vertically above the centre of the sphere. The other end of the string is connected to a small particle of mass m that rests on the sphere. The string makes an angle alpha = 30^(@) with the vertical. Find the acceleration of the sphere immediately after it is released. There is no friction anywhere.

Two hemispheres of radii R and r(lt R) are fixed on a horizontal table touching each other (see figure). A uniform rod rests on to spheres as shown. The coefficient of friction between the rod and two spherers is mu . Then the maximum value of the ratio (r)/(R) for which the rod will not slide is :

Two hemispheres of radii R and r(lt R) are fixed on a horizontal table touching each other (see figure). A uniform rod rests on to spheres as shown. The coefficient of friction between the rod and two spherers is mu . Then the maximum value of the ratio (r)/(R) for which the rod will not slide is :

A sphere of mass M is held at rest on a horizontal floor. One end of a light string is fixed at a point that is vertically above the centre of the sphere. The other end of the string is connected to a small particle of mass m that rest one the sphere. The string makes an angle alpha = 30^(@) with the vertical. Then the acceleration of the spherer immediately after it is released is : (There is no frication anywhere and string is tangene to the sphere) :

A sphere of mass M is held at rest on a horizontal floor. One end of a light string is fixed at a point that is vertically above the centre of the sphere. The other end of the string is connected to a small particle of mass m that rest one the sphere. The string makes an angle alpha = 30^(@) with the vertical. Then the acceleration of the spherer immediately after it is released is : (There is no frication anywhere and string is tangene to the sphere) :

A uniform rod of length l and mass 2m rests on a smooth horizontal table. A point of mass m moving horizontally at right angle to the rod with velocity v collides with one end of the rod and sticks to it, then: