# NCERT Physics Class 11 Exemplar Ch 7 System Of Particles And Rotational Motion Part 6

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## Very Short Answer

Q.21. A door is hinged at one end and is free to rotate about a vertical axis (Fig.). Does its weight cause any torque about this axis? Give reason for your answer.

Answer: No. A force can produce torque only along a direction normal to itself as . So, when the door is in the xy-plane, the torque produced by gravity can only be along direction, never about an axis passing through y direction.

Q.22. ) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.

Answer: Let the C.M. be ‘b’. Then,

## Long Answer

Q.24. Two discs of moments of inertia about their respective axes (normal to the disc and passing through the center), and rotating with angular speed are brought into contact face to face with their axes of rotation coincident.

(a) Does the law of conservation of angular momentum apply to the situation? why?

Answer: Yes, because there is no net external torque on the system. External forces, gravitation and normal reaction, act through the axis of rotation, hence produce no torque.

(b) Find the angular speed of the two-disc system.

Answer: By angular momentum conservation

(c) Calculate the loss in kinetic energy of the system in the process.

Answer:

(d) Account for this loss.

Answer: The loss in kinetic energy is due to the work against the friction between the two discs.

Q.25. A disc of radius R is rotating with an angular speed about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is

(a) What was the velocity of its centre of mass before being brought in contact with the table?

Answer: Zero

(b) What happens to the linear velocity of a point on its rim when placed in contact with the table?

Answer: Decreases

(c) What happens to the linear speed of the center of mass when disc is placed in contact with the table?

Answer: Increases

(d) Which force is responsible for the effects in (b) and (c).

Answer: Friction

(e) What condition should be satisfied for rolling to begin?

Answer:

(f) Calculate the time taken for the rolling to begin.

Answer: Acceleration produced in Centre of mass due to friction:

Angular acceleration produced by the torque due to friction,

For rolling without slipping,