Two particles A and B, of masses 3m kg and 2m kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a plane. The plane is inclined at an angle θ to the horizontal. A lies on the plane and B hangs vertically, 0.8 m above the floor, which is horizontal. The string between A and the pulley is parallel to a line of greatest slope of the plane (see diagram). Initially A and B are at rest.

A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the poi...

A cylindrical container is open at the top. The curved surface and the circular base of the container are both made f...

A particle P is projected with speed 20 m s¯¹ at an angle of 60° below the horizontal, from a point O which is 30 m a...

The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.

The variables x and θ satisfy the differential equation x cos² θ (dx/dθ) = 2 tan θ + 1, for 0 ≤ θ < ½π and x > 0. It ...