A block of mass 2 kg moving on a horizontal surface with speed of 4 ms^$$-$$1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = $$-$$kx where k = 12 Nm^$$-$$1. The speed of the block as it just crosses the rough surface will be :

A $$\sqrt {34} $$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If E_f and F_w are the reaction forces of the floor and the wall, then ratio of $${F_w}/{F_f}$$ will be :

(Use g = 10 m/s².)

Water falls from a 40 m high dam at the rate of 9 $$\times$$ 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is :

(Take g = 10 ms^$$-$$2)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :