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As it is, the system above is not balanced. Which of the followingchanges would NoT balance the system so that there is o net torque?Assume the plank has no mass of its own.(A) Adding a mass equal to $m_{2}$ on the far left side and a mass equal to(B) Stacking both masses directly on top of the fulcrum(C) Moving the fulcrum a distance L/3 to the right(D) Moving both masses a distance L/3 to the left

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Chapter 1

Practice Test 1

Section 1

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Hi in the given problem a mask less been is he voted at a program? Yeah, like this at the center. Now this beam is divided into four equal parts, each having a length of L. Now there are two particles of masses and one & M. two which will be providing their wits vertically downward and one G. And M two G. At the given points here this is given that and one M two is twice massive As that of M1. Its mouth is twice As that of M one M 2. M one. So the clockwise torque on this bean will be more than the counterclockwise stark. So in the given situation, the clockwise dark acting on this beam will be given by The weight M two G. Multiplied by its perpendicular, transformed the program which is L. And for them to we can use twice off M1 so it becomes twice off. EM Burn G. L. And counter clockwise torque will be given by M one G. multiplied by its botanical distance from the Fulcrum, which is just L. So this is M one G. L. hands. It is clear that the clockwise stock is more than the counterclockwise talk. So this being will be having a tendency to rotate clockwise. Now. In the four given options, we have to make some arrangements. Two bring the beam in equilibrium, rotational equilibrium. Then we have to select the option which will not bring the beam in equilibrium. So here in option a we have to put Hamas, M two At the far left hand means here must M2. So the total counter clockwise torque will come out to be, let it be to one is equal to M two G into perpendicular distance, which will be L plus L means to well. And the original talk Created by the originally present mass and one that is Edwin G. L.. Now as you know, M two equals two twice of heaven. So this is twice of em bong into two L plus M one G L. So it comes out to be five M one GL. No, if you look for the block way start for which there is a mask. I am one that has been placed at the far right end of the beam must them to hear. So now the total clock by Stark will be given by M one G into two L plus the originally present mars was um been in two GL. So finally it comes out to be how to Is equal to four M 1 GL. So as the counterclockwise dot is five MG L. And one jail. And clockwise talk is M one for em and G. So we can say that being is not in a rotational equilibrium. Now, if we look for the option B. Yeah, We are stacking both the masses M1 and M2 directly on the Fulcrum, so doing this, the beam will come and rotational equilibrium, so that being will be balanced. Now, option C. We are moving Fulcrum to the right by L x three here, in this regard, if this fulcrum is shifted towards right here By our the stance of L x three, no other change is made there. So for the clock by stork, Mtg will be multiplied by this distance, which will be L minus Y. Three, and M and G will be multiplied by this distance, which will be L plus L by three. So now the counterclockwise talk will become M one G into L plus L by tree, which will come out to be four M one G. L by three. And counterclockwise and clockwise. Start out too will come out to be M two G into l minus alibi tree for them to again this is two M. One to M one G. Into to L by three again which will come out to be four M one G. L by three. Mr Bean will be balanced in this case. Also now the last case D. This time we are moving both the masses L by three to the left, so doing this, the counter clockwise torque Taiwan will be M one G. And we have shifted it towards the left. So its distance from Fulcrum will be increased by el by three. So it will come out to be four M one G. L x three and clock my store the mass the world Mtg it will be a less distance from the fulcrum. So so it will be l minus L by three and M. Two. We know that is equal to gamble. So the is to mong into L by three. So that is again four M one G. L by three. So again the being will be balanced. Hands only correct option in which the being will not be balanced is option A. Thank you.

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