A thin rod of mass `m` and length `2l` is placed horizontally and perpendicular to a horizontal rough nail, as shown in figure and set free. The point of contanct of the rod with the nails is `l//3` distance away form the centre of rod. If the rod starts slipping when it forms an angle `theta` with the horizontal and the coefficient of friction of rod with nails is `mu`, then find `(mu)/(tan theta)`.

A uniform rod of length 2a is placed horizontally on the edge of a table. Initially the centre of mass of the rod is at a distance a//3 from the edge. The rod is released from rest. If the rod slips after it turned an angle theta , find the coefficient of friction between the rod and the table.

A uniform thin rod of mass m and length l is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes an angle theta with horizontal.

A uniform thin rod of mass m and length l is standing on a smooth horizontal suface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes an angle theta with horizontal.

A uniform thin rod of mass m and length l is standing on a smooth horizontal suface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes an angle theta with horizontal.

One-fourth length of a uniform rod of mass m and length l is placed on a rough horizontal surface and it is held stationary in horizontal position by means of a light thread as shown in the figure. The thread is then burnt and the rod start rotating about the edge. Find the angle between the rod and the horizontal when it is about to slide on the edge. The coefficient of friction between the rod and surface is mu .

One-fourth length of a uniform rod of mass m and length l is placed on a rough horizontal surface and it is held stationary in horizontal position by means of a light thread as shown in the figure. The thread is then burnt and the rod start rotating about the edge. Find the angle between the rod and the horizontal when it is about to slide on the edge. The coefficient of friction between the rod and surface is mu .

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the intial angular acceleration of the rod is

A uniform rod of mass m and length l is at rest on smooth horizontal surface. An impulse P is applied to end B as shown. Distance travelled by the centre of the rod, while rod rotates by 90^(@)