A thin rod MN free to rotation in the vertical plane about the fixed end N is held horizontal when the end M is released the speed of this end when the rod makes an anle `alpha` with the horizontal will be proportional to : (see figure)

In the figure shown one end of a light spring of natural length l_(0)=sqrt(5/8)m(~~0.8m) is fixed at point D and other end is attached to the centre B of a uniform rod AF of length l_(0)//sqrt(3) and mass 10kg. The rod is free to rotate in a vertical plane about a fixed horizontal axis passing through the end A of the rod. The rod is held at rest in horizontal position and the spring is in relaxed state. It is found that, when the rod is released to move it makes an angle of 60^(@) with the horizontal when it comes to rest for the first time. Find the (a) the maximum elogation in the spring . (Approximately) (b) the spring constant. (Approximately)

In the figure shown one end of a light spring of natural length l_(0)=sqrt(5/8)m(~~0.8m) is fixed at point D and other end is attached to the centre B of a uniform rod AF of length l_(0)//sqrt(3) and mass 10kg. The rod is free to rotate in a vertical plane about a fixed horizontal axis passing through the end A of the rod. The rod is held at rest in horizontal position and the spring is in relaxed state. It is found that, when the rod is released to move it makes an angle of 60^(@) with the horizontal when it comes to rest for the first time. Find the (a) the maximum elogation in the spring . (Approximately) (b) the spring constant. (Approximately)

A rod length L is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle theta with horizontal the velocity of COM of the rod is v_(0) . The velocity of the end of the rod in contact with the surface at that instant is:

A light rigid rod of length l is constrained to move in a vertical plane, so that its ends are along the x and y axes respectively. Find the instantaneous axis of rotation of the rod when it makes an angle theta with horizontal.

A light rigid rod of length l is constrained to move in a vertical plane, so that its ends are along the x and y axes respectively. Find the instantaneous axis of rotation of the rod when it makes an angle theta with horizontal.

A uniform rod of length l and mass M pivoted about its end as shown in Fig. and is free to rotate in the vertical plane about the pivot. The rod is released from rest in the horizontal position. (a) What is the initial angular acceleration of the rod? (b) Find the initial acceleration of the right end of the rod? ( c) Find normal contact force due to hinge when rod has rotated through angle theta as shown in Fig.

A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle theta with the vertical is

A rod of length L is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At at certain instant of time, when the rod makes an angle 37^@ with horizontal the velocity of COM of the rod of 2m//s . The velocity of the end of the rod in contact with the surface at that instant is

A rod of length L is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At at certain instant of time, when the rod makes an angle 37^@ with horizontal the velocity of COM of the rod of 2m//s . The velocity of the end of the rod in contact with the surface at that instant is