A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m.

(Assume there is no friction between the block and the hemisphere)

A force of F = (5y + 20)$$\widehat j$$ N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is ___________ J.

In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is _________ m. (g = 10 m/s²).

A ball of mass 4 kg, moving with a velocity of 10 ms^$$-$$1, collides with a spring of length 8 m and force constant 100 Nm^$$-$$1. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.