Curves:- Cycloid
Q.1 A circle of 50 mm diameter rolls on a horizontal line for a half revolution & then on a vertical line for another half revolution. Draw the curve traced out by a point P on the circumference of the circle . Name the curve . Draw tangent and normal at a point 25 mm away from the horizontal line.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
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