NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotation Motion-Part 17

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Question 7.23:

A man stands on a rotating platform, with his arms stretched horizontally holding a weight in each hand. The angular speed of the platform is . The man then brings his arms close to his body with the distance of each weight from the axis changing from . The moment of inertia of the man together with the platform may be taken to be constant and equal to

(a) What is his new angular speed? (Neglect friction)

(b) Is kinetic energy conserved in the process? If not, from where does the change come about?

Answer:

(a) New angular speed:

Explanation:

Angular speed:

Figure shown the angular speed,

angular speed is shown in figure.

Figure Shown the Angular Speed

angular speed is shown in figure.

Moment of inertia of the man-platform system

Moment of inertia when the man stretches his hands to a distance of

Initial moment of inertia of the system,

Angular speed,

Angular momentum,

Moment of inertia when the man folds his hands to a distance of

Final moment of inertia,

Final angular speed

Final angular momentum,

From the conservation of angular momentum, we have:

(b) Is kinetic energy conserved in the process:

Kinetic energy is not conserved in the given process. In fact, with the decrease in the moment of inertia, kinetic energy increases. The additional kinetic energy comes from the work done by the man to fold his hands toward himself.

Question 7.24:

A bullet of mass and speed is fired into a door and gets embedded exactly at the centre of the door. The door is wide and weighs . It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it. (Hint: The moment of inertia of the door about the vertical axis at one end is .)

Answer:

Mass of the bullet,

Velocity of the bullet,

Thickness of the door,

Radius of the door,

Mass of the door,

Angular momentum imparted by the bullet on the door:

Moment of inertia of the door:

But,