A horse runs along a circle with a speed of `20k m//h` . A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Find the speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/h.

For a particle, revolving in a circle with speed, the acceleration of the particle is (a) along the tangent

. Let A be the centre of the circle x^2+y^2-2x-4y-20=0 Suppose that the tangents at the points B(1,7) and D(4,-2) on the circle meet at the point C. Find the area of the quadrilateral ABCD

A particle moves in a circle of radius 20 cm with linear speed of 10 m/s. Find the angular velocity

The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle x^2+y^2-8x+6y+20=0 . Find the coordinats of the corresponding point of contact.

The sphere shown in figure lies on a rough plane when a particle of mass m travelling at a speed v_0 collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find a. the linear speed o the combined system just after the collision b. the angular speed of the system about the centre of the sphere just the collision c. the value of h for which the sphere starts pure rolling on the plane Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere.

Figure shows a mass m placed on a frictionless horizontal table and attached toa string passing through a mall hole in the surface. Initially, themas movesin a circle of radius r_0 with a speed v_0 and the ree end of the string is held by a person. The person pulls on the string slowly to decrease the radius of th circle of r. a. Find the tension in the string when the mass moves in the circle of radius r. b. Calculate the chasnge in the kinetic energy of the mass

A particle from the point P(sqrt3,1) moves on the circle x^2 +y^2=4 and after covering a quarter of the circle leaves it tangentially. The equation of a line along with the point moves after leaving the circle is

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. The impressed force on the same is in which direction?