Curves:- Helix & Spirals

Q.1 An inelastic string of 100 mm length is wound round a cylinder of 50 mm diameter keeping the string always tight. Draw the curve generated by end point of the string. Name the Curve.
Q.2 A point P is moving around the surface of a cone of base 80 mm & height 90 mm. If the point P starting from the apex, reaches the periphery of cone base, in one and half turns. Draw the projection of the path of P. Assume that the axial descent of the point in uniform with its rotation.
Q.3 A right Angle triangle of two sides 33 mm and 53 mm & hypotenuse 62.5 mm is rotating around side of 53 mm. A point P is moving up on the hypotenuse. During the rotation of the triangle point P moves from the bottom most position to highest position on hypotenuse while the triangle completes one revolution. Both the movements are uniform. Draw the path of the point P in elevation & Plan. Name the curve of plan & curve of elevation.
Q.4 Draw one convolutions of the Archimedean spiral represented by the polar equation
r = 32 + 7 * θ , where r is in mm and θ is in radian. Draw the tangent and normal to the curve at point 55 mm from the pole.
Q.5 A pendulum oscillates in a plane through an angle of 200 on either side of the plumb line & makes one oscillation .During this period , an ant moves on the pendulum from bottom end to top with uniform velocity. Trace the path of the ant.
Q.6 A straight line AB of 60 mm length rotates clockwise about its end A for one complete revolution & during this period, a point P moves along the straight line from A to B & returns back to the point A .if the rotary motion of the straight line about point A & linear motion of point P along AB are both uniform, draw the path of the point P . Name the curve. Draw Normal & Tangent to the curve at a point 35 mm from the point A.
Q.7 Draw a triangle AOB with OA=30 mm, OB=50 mm & AOB =120 0. Draw an Archimedean spiral passing through points A & B with O as a pole. Complete the curve starting from O. Also draw tangent & normal to the curve at a distance of 27 mm from O. (Refer Jolhe PN 6.37)