Rotation 3 Question 13

19. The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2.

The ring and disc are separated by frictionless ball bearings. The system is in the xz plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30 with the horizontal. Then with respect to the horizontal surface,

(2012)

(a) the point O has a linear velocity 3Rωi^

(b) the point P has a linear velocity 114Rωi^+34Rωk^

(c) the point P has a linear velocity 134Rωi^34Rωk^

(d) the point P has a linear velocity

334Rωi^+14Rωk^

Show Answer

Answer:

Correct Answer: 19. (a,b)

Solution:

  1. Velocity of point O is

vO=(3Rω)i^

vPO is Rω2 in the direction shown in figure.

In vector form

vPO=Rω2sin30i^+Rω2cos30k^=Rω4i^+3Rω4k^vPO=vPvOvP=vPO+vO=Rω4i^+3Rω4k^+3Rωi^=114Rωi^+34Rωk^



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक