The free end of a thread wound on a bobbin is passed round a nail A hammered into the wall. The thread is pulled at a constant velocity 'v' . Assuming pure rolling of bobin, find the velocity `v_(0)` of the centre of the bobbin at the instant when the thread forms an angle `alpha` with the vertical: (`R` and `r` are outer and inner radii off the babbin)

Figure shows a rod of length l resting on a wall and the floor. Its lower end A is pulled towards left with a constant velocity v. Find the velocity of the other end B downward when the rod makes an angle theta with the horizontal.

End A of a rod AB is being pulled on the floor with a constant velocity v_(0) as shown. Taking the length of the rod as l , at an instant when the rod makes an angle 37^@ with the horizontal, calculate the velocity of the CM of the rod

A light thread is tightly wrapped around a fixed disc of radius R. A particle of mass m is tied to the end P of the thread and the vertically hanging part of the string has length piR . The particle is imparted a horizontal velocity V=sqrt((4pigR)/3) . The string wraps around the disc as the particle moves up. At the instant the velocity of the particle makes an angle of theta=60^(@) with horizontal, calculate. (a) Speed of the particle (b) Tension in the string

A uniform circular loop of radius a and resistance R is pulled at a constant velocity v out of a region of a uniform plane of the loop and the velocity are both perpendicular to B. Then the electrical power in the circular loop at the instant when the arc (of the circular loop) outside the region of magnetic field subtends an angle (pi)/(3) at the centre of the loop is

A projectile, thrown with velocity v_(0) at an angle alpha to the horizontal, has a range R. it will strike a vertical wall at a distance R//2 from the point of projection with a speed of

A particle of mass m moves along the internal smooth surface of a vertical cylinder of the radius R. Find the force with which the particle acts on the cylinder wall if at the initial moment of time its velocity equals v_(0) . And forms an angle alpha with the horizontal.