NCERT Physics Class 11 Exemplar Ch 7 System of Particles and Rotational Motion Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q. 26. Two cylindrical hollow drums of radii and of a common height h, are rotating with angular velocities ω (anti-clockwise) and ω (clockwise) , respectively. Their axes, fixed are parallel and in a horizontal plane separated by . They are now brought in contact

(a) Show the frictional forces just after contact.

Answer:

(b) Identify forces and torques external to the system just after contact.

Answer: where F and F ″ and external forces through support.

External torque , anticlockwise.

(c) What would be the ratio of final angular velocities when friction ceases?

Discs in Contact

Answer: Let ω1 and ω2 be final angular velocities (anticlockwise and clockwise respectively)

Finally there will be no friction.

Hence,

Q. 27. A uniform square plate S (side c) and a uniform rectangular plate R (sides b, a) have identical areas and masses (Fig.) .

Moment of Intertia

Show that

Answer: Area of square = area of rectangle ➾

Answer:

And

Answer:

Q. 28. A uniform disc of radius R, is resting on a table on its rim. The coefficient of friction between disc and table is μ (Fig.) . Now the disc is pulled with a force F as shown in the figure. What is the maximum value of F for which the disc rolls without slipping?

Slipping Disc

Answer: Let the acceleration of the Centre of mass of disc be ‘a’ , then

The angular acceleration of the disc is . (if there is no sliding) .

Then

Thus, Since there is no sliding,