00:02
In this question there are two bodies that is a and b and they are connected by a pulley here okay and you can see that this is the body a this is body b let i assume that mass of body a is capital m and mass of body b is small m okay i am writing here mass of a is capital m and mass of b is small m okay and t is tension in the string here okay and acceleration is taken as small a okay these are the things i had assumed here and now we are going on our question here okay capital m is provided to us that is 5kg small m is 3kg and acillization we had to calculate and mu that is friction coefficient is provided to us that is 0 .10 okay now we move on our question you can see here if i make a free body diagram for the object b then due to its mass it applies weight on downward and there is a string in there there must be a overall finally since m g is greater than t it is having a downward fall here okay with some force that is small m a okay now by applying the force equilibrium here we can say that m a should be equals to m g minus t okay this is equation number one now i apply free body diagram for the object that is a okay it is lying on the flat surface which is having a friction that is friction coefficient 0 .10.
02:06
Now you see that it is also having some mass due to which mg applies on downward and due to this the table applies a reaction force on the upwards direction that is n.
02:17
Okay and you can see that there is a string here and due to this string there must be a tension and in the opposite direction there due to the friction there is mu and that is mew and that is a string and that is a tension and that is friction force okay and this body will also start sliding with an acceleration that is we had assumed a so finally you can see that after all this body is going to slide here with an acceleration a so the force should be equals to capital m into a here also we have to take capital m because mass is in capital m for body a now we apply the force equilibrium for this one then you can see that there is a tension on the straight direction and there is a friction force on the opposite direction so the friction opposes the motion but the tension is later than friction so tension minus friction force provides the acceleration that is m a okay this is equation number two now here n is the reaction force that is due to weight that is i can say that capital m g okay so t minus mu into capital m g m g equals to capital m .a.
03:35
Now you can see that this is our second equation.
03:39
Now we have to find with the help of first and second equation value of small a and value of capital t.
03:47
So i am going to add both the equations of first and second.
03:52
So you can see that by adding equation first and second what happens? we have mg minus t that is a.
04:02
Added with t minus mu m g so m g minus t is added with t minus mu m g equals to small m a plus capital m a okay small m a plus capital m a now you see here your t cancel outs and from these terms we can take common that is our m here okay no we cannot take it common because it is having small m and it is having capital m okay equals to take here a common then you get small m plus capital m now from here we get the value of a that is m g minus mu capital m divided by small m plus capital m now i put all the values here small m is mass of object b that is 3 into g is 9 .8 minus mu is 0 .10 into capital m mass of a that is 5 into g is 9 .8 and divided by 3 plus 5 okay after solving it we get the value of acceleration that is 3 .0625 meter per second is square okay this is the value of acceleration and now we have to find the tension in the string to find it we can use any of the equation i am using equation first okay equation first was small m g minus t equals to small m a from here t must be equals to m g minus m a means take m common then g minus a now provide here all the values m is the mass of object b that is 3 into g is 9 .8 minus acceleration we had calculated is 3 .0625 after solving it we get 20 .212 new this is the value of tension in the string.
06:06
Now it is told that the object b that is falling down, okay? the object b that is falling down with an acceleration of a here, what does the height? it should travel, okay? let it is going to travel a height that is h, okay, and that is in three seconds it is provided to us...