The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

The following bodies,

(1) a ring

(2) a disc

(3) a solid cylinder

(4) a solid sphere,

of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ___________. [Mark the body as per their respective numbering given in the question]

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]