NCERT Physics Class 11 Exemplar Ch 7 System Of Particles And Rotational Motion Part 7

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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

Discs in Contact

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

Moment of Intertia

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

Slipping Disc

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,

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