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/s²)

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be $${1 \over 2}\sqrt {xgh} $$ m/s. The value of x is ___________.

A diatomic gas ($$\gamma$$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.