A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The acceleration of the disc will be $${2 \over b}$$g sin$$\theta$$ where b is ____________. (Round off to the Nearest Integer) (g = acceleration due to gravity, $$\theta$$ = angle as shown in figure)

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around is periphery as shown in the figure.


Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s^$$-$$1.

The value of n, to the nearest integer, is __________.

[Given : In one complete revolution, the disk rotates by 6.28 rad]

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P $$ of magnitude 100 N is applied at point A of the frame.


Suppose the force is $$\overrightarrow P $$ resolved parallel to the arms AB and AC of the frame.

The magnitude of the resolved component along the arm AC is xN.

The value of x, to the nearest integer, is ___________.

[Given : sin(35$$^\circ$$) = 0.573, cos(35$$^\circ$$) = 0.819

sin(110$$^\circ$$) = 0.939, cos(110$$^\circ$$) = $$-$$ 0.342 J

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s²)