Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds u₁ and u₂, respectively. The values of u₁ and u₂ are nearly :

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁, while water rises by the same amount h in a capillary tube of radius r₂. The ratio, (r₁/r₂), is then close to :

The value of acceleration due to gravity at Earth's surface is 9.8 ms^–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms^–2, is close to : (Radius of earth = 6.4 × 10⁶ m)

A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :