A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $${x \over 5}$$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $$\theta$$ = tan^{$$-$$1} (x $$\times$$ 10^{$$-$$1}). The value of x is ____________.

(Given, g = 10 m/s^{2})

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7^{th} and 8^{th} ball is __________ N when 6^{th} ball just leaves the table.

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $$\sqrt{x}$$N as shown in figure.

The value of x = _____________.