Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

34 Aptitude Test Problems in Physics

Determine the minimum initial velocity

vo at which the body starts moving upwards

without being separated from the surface

of the pipe.

Fig. 33

1.67*. An inextensible rope tied to the axle

of a wheel of mass m and radius r is pulled

in the horizontal direction in the plane

of the wheel. The wheel rolls without jump-

ing over a grid consisting of parallel hori-

zontal rods arranged at a distance 1 from

one another (1 < r).

Determine the average tension T of the

rope at which the wheel moves at a constant

velocity v, assuming the mass of the wheel

to be concentrated at its axle.

1.68. Two coupled wheels (i.e. light wheels

of radius r fixed to a thin heavy axle)

roll without slipping at a velocity v per-

pendicular to the boundary over a rough

horizontal plane changing into an inclined

plane of slope a (Fig. 34).

Determine the value of v at which the

coupled wheels roll from the horizontal to

the inclined plane without being separated

from the surface.