Answer
Verified
89.7k+ views
Hint: We can find the shift within the center of mass because the product of mass removed and therefore the distance between original center of mass and away from each other when divided by the mass of the remaining portion is also known as centre of mass.
Complete step by step answer:
The center of mass of the primary arrangement is six equal masses on the six corners of a regular hexagon side length and is at the center of the hexagon. Then the new arrangement if the mass of one of the particles is doubled, and find the value of the shift in the center of mass.
The total masses will be $6m + m = 7m$.
When, the six identical particles are present at six different positions of the hexagon. So, the moment will be $2m \times L$ for that shifted particle. So, the total will be
$\dfrac{2mL+\dfrac{-mL}{2}+\dfrac{-mL}{2} +mL-mL}{7m}$
$ \Rightarrow \dfrac{{2mL - mL}}{{7m}}$
Which one is solving we will get the value of position of the center is,
$ \Rightarrow \dfrac{L}{7}$
Since, the masses are the same for all positions except the shifted mass of $2m$ hence the moment can be added.
Hence, the correct answer is option (C).
Additional Information:
A scientific method for locating the middle of mass is to suspend the thing from two locations and to drop plumb lines from the suspension points. The intersection of the 2 lines is that the centre of mass. The shape of an object might already be mathematically determined, but it's getting to be too complex to use a known formula.
Note: Shift in Centre of Mass, when the certain mass is removed. If a particular mass from the system is removed, the centre of mass obviously changes from its existing position. When some mass of the system is removed, a new centre of mass shifts towards the heavier a neighbourhood of the system.
Complete step by step answer:
The center of mass of the primary arrangement is six equal masses on the six corners of a regular hexagon side length and is at the center of the hexagon. Then the new arrangement if the mass of one of the particles is doubled, and find the value of the shift in the center of mass.
The total masses will be $6m + m = 7m$.
When, the six identical particles are present at six different positions of the hexagon. So, the moment will be $2m \times L$ for that shifted particle. So, the total will be
$\dfrac{2mL+\dfrac{-mL}{2}+\dfrac{-mL}{2} +mL-mL}{7m}$
$ \Rightarrow \dfrac{{2mL - mL}}{{7m}}$
Which one is solving we will get the value of position of the center is,
$ \Rightarrow \dfrac{L}{7}$
Since, the masses are the same for all positions except the shifted mass of $2m$ hence the moment can be added.
Hence, the correct answer is option (C).
Additional Information:
A scientific method for locating the middle of mass is to suspend the thing from two locations and to drop plumb lines from the suspension points. The intersection of the 2 lines is that the centre of mass. The shape of an object might already be mathematically determined, but it's getting to be too complex to use a known formula.
Note: Shift in Centre of Mass, when the certain mass is removed. If a particular mass from the system is removed, the centre of mass obviously changes from its existing position. When some mass of the system is removed, a new centre of mass shifts towards the heavier a neighbourhood of the system.
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
Choose the incorrect statement from the following A class 12 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
A pendulum clock keeps the correct time at 20 degrees class 11 physics JEE_Main
Assertion The trajectory of a projectile is quadratic class 11 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Ethylidene dichloride is obtained by the reaction of class 12 chemistry JEE_Main