Answer

Verified

78.9k+ views

**Hint:**We know that momentum is a physics term that refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum. One example is the use of air bags in automobiles. Air bags are used in automobiles because they are able to minimize the effect of the force on an object involved in a collision. Air bags accomplish this by extending the time required to stop the momentum of the driver and passenger. Momentum is mass in motion, and any moving object can have momentum. An object's change in momentum is equal to its impulse. Impulse is a quantity of force times the time interval. Impulse is not equal to momentum itself; rather, it's the increase or decrease of an object's momentum. Based on this concept we have to solve this question.

**Complete step by step answer**

Given,

A particle having mass $=\mathrm{m}$

length $=\mathrm{L}$

Mass of the bead is $2 \mathrm{m}$

since no force acts on the horizontal direction

So, the center of mass the beard and the particle should remain at the same x-coordinate.

Since no force acts on the horizontal direction.

So, the center of mass the beard and the particle should remain at the same x-coordinate.

We have a mass of bead is $2 \mathrm{m}$ and make an angle $\theta$ with the wire Initial x-coordinate of the center of mass from the original position of the bead is:

$=\dfrac{2 \mathrm{m} \times 0+\mathrm{m} \times 1}{3}$

$=\dfrac{\mathrm{L}}{3 \mathrm{m}} \ldots 1$

Now the final position of the center of mass if bead has moved by a distance:

$=\dfrac{[2 \mathrm{mx}+\mathrm{m}(\mathrm{x}+\mathrm{Lcosa})]}{3 \mathrm{m}}$

$=\dfrac{3 \mathrm{x}+\mathrm{Lcosa}}{3 \mathrm{m}} \ldots 2$

By solving equation 1 and 2 then we get,

$3 x+L \cos a=L$

$\mathrm{x}=\dfrac{\mathrm{L}(1-\cos \mathrm{a})}{3}$

**Hence the correct answer is option C.**

**Note:**We should know that linear momentum is defined as the product of a system's mass multiplied by its velocity. In symbols, linear momentum is expressed as$p=mv$. Momentum is directly proportional to the object's mass and also its velocity. Thus, the greater an object's mass or the greater its velocity, the greater its momentum. Note that the linear moment is a vector quantity and is conserved in any direction. In the center-of-mass system, the total momentum is always zero, before and after the interaction, in any direction. Angular momentum is inertia of rotation motion. Linear momentum is inertia of translation motion. The big difference is that the type of motion which is related to each momentum is different. It is important to consider the place where the force related to rotation applies, which is appears as 'r' in the formula

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

The IUPAC name of the following compound is A Propane123tricarbonitrile class 12 chemistry JEE_Main

Choose the correct statements A A dimensionally correct class 11 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main