NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotational Motion Part 5

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Question 7.14:

A rope of negligible mass is wound round a hollow cylinder of mass and radius . What is the angular acceleration of the cylinder if the rope is pulled with a force of ? What is the linear acceleration of the rope? Assume that there is no slipping.

Answer:

Mass of the hollow cylinder,

Radius of the hollow cylinder,

Applied force,

The moment of inertia of the hollow cylinder about its geometric axis:

Torque,

For angular acceleration , torque is also given by the relation:

Linear acceleration

Question 7.15:

To maintain a rotor at a uniform angular speed of , an engine needs to transmit a torque of . What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is efficient.

Answer:

Angular speed of the rotor,

Torque required,

The power of the rotor is related to torque and angular speed by the relation:

Hence, the power required by the engine is

Question 7.16:

From a uniform disk of radius a circular hole of radius is cut out. The centre of the hole is at from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

Answer: , from the original centre of the body and opposite to the centre of the cut portion.

Explanation:

Mass per unit area of the original disc

Radius of the original disc

Mass of the original disc,

The disc with the cut portion is shown in the following figure:

The disc with the cut portion is shown in the following figu …

Figure Shown the Disc with the Cut Portion

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Radius of the smaller disc

Mass of the smaller disc,

Let and be the respective centres of the original disc and the disc cut off from the original. As per the definition of the centre of mass, the centre of mass of the original disc is supposed to be concentrated at , while that of the smaller disc is supposed to be concentrated at

It is given that:

After the smaller disc has been cut from the original, the remaining portion is considered to be a system of two masses. The two masses are: (concentrated at ), and

concentrated at

(The negative sign indicates that this portion has been removed from the original disc.) Let be the distance through which the centre of mass of the remaining portion shifts from point

The relation between the centers of masses of two masses is given as:

For the given system, we can write:

(The negative sign indicates that the centre of mass gets shifted toward the left of point .)