The collar `A` is free to slide along the smooth shaft `B` mounted in the frame. The plane of the frame is the vertical . Determine the horizontal acceleration a of the frame necessary to maintain the collar in a fixed position on the shaft. `(g = 9.8 m//s^(2))`

Two particles are projected from the same point, with the same speed, in the same vertical plane, at different angles with the horizontal.A frame of references is fixed to one particle.The position vector of the other particle as observed from this frame is vecr Which of the following statements are corrects?

A stone is thrown with an initial velocity components of 20 m/s along the vertical, and 15 m/s along the horizontal direction. Determine the position and velocity of the stone after 3 s. Determine the maximum height that it will reach and the total distance travelled along the horizontal on reaching the ground. (Assume g= 10 m//s^2 )

A stationary platform P which can rotate freely about a vertical axis (figure) supports a motor M and a balance weight N. The moment of inertia of the platform with the motor and the balance weight relative to this axis is equal to I. A light frame is fixed to the motor's shaft with a uniform sphere A rotating freely with an angular velocity omega_0 about a shaft BB^' coinciding with the axis OO^' . The moment of inertia of the sphere relative to the rotation axis is equal to I_0 . Find (a) the work performed by the motor in turning the shaft BB^' through 90^@ , through 180^@ , (b) the moment of external forces which maintains the axis of the arrangement in the vertical position after the motor turns the shaft BB^' through 90^@ .

A block of mass m is attached to the frame by a light spring of stiffness k . The frame and block are initially at rest with x=x_(0) , the uncompressed length of the spring. If the frame is given a constant horizontal acceleration a_(0) towards left, determine the maximum velocity (v_(ret))_(max) of the block relative to the frame (block is free to move inside frame). Ignore any friction.

Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle , as observed from this frame, is vecr . Which of the following statement is correct?

Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle , as observed from this frame, is vecr . Which of the following statement is correct?

An L shaped frame is free to rotate in a vertical plane about a horizontal axis passing through a smooth hinge O. Each side of the frame has a length L and mass m. Frame is let to fall with one side horizontal and the other vertical. Angular acceleration of the frame just after it is allowed to fall is

A 10 kg collar P slides with negligible friction on the fixed vertical shaft. When the collar is released from rest at the bottom position shown, it moves up the shaft under the action of the constant force F = 200 N applied to the cable. The position of the small pulley at B is fixed. Find the spring constant k (in k-N // m ) which the spring must have if its maximum compression is to be limited to 0.4 m.