﻿ A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. 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 ML2/3.) from Physics System of Particles and Rotational Motion Class 11 Manipur Board

## Chapter Chosen

System of Particles and Rotational Motion

## Book Store

Currently only available for.
`CBSE` `Gujarat Board` `Haryana Board`

## Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
`Class 10` `Class 12`
A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. 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 ML2/3.)

Given,

Mass of the bullet, m = 10 g = 10 × 10–3 kg

Velocity of the bullet, v = 500 m/s

Thickness of the door, L = 1 m

Radius of the door, r = m / 2

Mass of the door, M = 12 kg

Angular momentum imparted by the bullet on the door,

α = mvr

= (10 × 10-3 ) × (500) ×

=  2.5 kg m2 s-1                                   ...(i)

Moment of inertia of the door is given by,

This is the required angular speed of the door just after the bullet embeds into it.

267 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object.
911 Views

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system.
794 Views

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion.
943 Views

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated.
1449 Views

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
730 Views