A particle is resting on an inverted cone as shown. It is attached to cone by a thread of length 20 cm. String remains parallel to slope of cone. The cone is givenangular acceleration of `0.5 rad//sec^(2)` then at what time does mass leave contact with surface (assuming sufficient friction) :

A block of mass m height 2h and width 2b rests on a flat car which moves horizontally with constant acceleration a as shown in figure. Determine a. the value of the acceleration at which slipping of the block on the car starts, if the coefficient of friction is mu . b. the value of the acceleration at which block topples about A , assuming sufficient friction to prevet slipping and c. the shortest distance in which it can be stopped from a speed of 20 ms^(-1) with constant deceleration so that the block is not disturbed. The following data are given b=0.6 m, h=0.9m, mu=0.5 and g=10ms^(-2)

A block of mass m height 2h and width 2b rests on a flat car which moves horizontally with constant acceleration a as shown in figure. Determine a. the value of the acceleration at which slipping of the block on the car starts, if the coefficient of friction is mu . b. the value of the acceleration at which block topples about A , assuming sufficient friction to prevet slipping and c. the shortest distance in which it can be stopped from a speed of 20 ms^(-1) with constant deceleration so that the block is not disturbed. The following data are given b=0.6 m, h=0.9 mu=0.5 and g=10ms^(-2)

One twirls a circular ring (of mass and radius ) near the tip of one’s finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is ?. The finger rotates with an angular velocity 2_(0). The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is mu and the acceleration due to gravity is g. The minimum vlaue of omega_(0) below which the ring will drop down is

A samll object of mass 10.0 g is at rest 30.0 cm from a horizontal disk's centre. The disk starts to rotate from rest about its centre with a constant angular acceleration of 4.50 rad/ s^(2) . What is the magnitude of the net force acting on the object after a time of t=1/3 s if the object remains at rest with respect to the disk ?

A massless spring of stiffness 400 N/m is fastened at left end to a vertical wall as shown in the figure I. initially block C of mass 2 kg and block D of mass 5 kg rest on horizontal surface with block C in contact with spring (But not compressiong it.) and the block D in contact with block C block C is moved leftward compressing spring by a distance of 0.5 m and held in place while block D remains at rest as shown in the figure. Now block C is released and it accelerates to the right towards block D the surface is rough and the coefficient of friction between each block and surface is 0.1 The block collide Instantaneously stick together and move right find the velocity of combined system just after collision.

A massless spring of stiffness 400 N/m is fastened at left end to a vertical wall as shown in the figure I. initially block C of mass 2 kg and block D of mass 5 kg rest on horizontal surface with block C in contact with spring (But not compressiong it.) and the block D in contact with block C block C is moved leftward compressing spring by a distance of 0.5 m and held in place while block D remains at rest as shown in the figure. Now block C is released and it accelerates to the right towards block D the surface is rough and the coefficient of friction between each block and surface is 0.1 The block collide Instantaneously stick together and move right find the velocity of combined system just after collision.

From the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base of the original cone. Find the total surface area of the remaining solid. [use pi=3.14,sqrt(5)=2.236 ]

A round cone A of mass m=3.2kg and half-angle alpha=10^@ rolls uniformly and without slipping along a round conical surface B so that its apex O remains stationary (figure). The centre of gravity of the cone A is at the same level as the point O and at a distance l=17cm from it. The cone's axis moves with angular velocity omega . Find: (a) the static friction force acting on the cone A, if omega=1.0rad//s , (b) at what values of omega the cone A will roll without sliding, if the coefficient of friction between the surfaces is equal to k=0.25 .

A small sized mass m is attached by a massless string (of length L ) to the top of a fixed frictionless solid cone whose axis is vertical. The half angle at the vertex of cone is theta. If the mass m moves around in a horizontal circle at speed v , what is the maximum value of v for which mass stay in contact with the comes? (g is acceleration due to gravity.)