 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of a length. First is 10 cm, second is 15 cm and third is 21 cm. So let this be a pendulum which swings this manner and this is an arc of a circle and let its length be denoted by capital R. And we are given that the length of the pendulum is 75 cm. Now let us begin with the solution. Now as we know length of arc is equal to 2 pi r into theta degrees upon 360. Length of the arc which we have denoted by capital R is equal to 2 pi r into theta degrees upon 360. So this formula implies that theta degree is equal to r into 360 upon 2 pi r and since 1 degree is equal to pi upon 180 radian, so this implies that the square root is equal to r into 360 upon 2 pi r into pi upon 180 radian pi cancels out with pi 0 with 0 18, 2s are 36, 2 cancels out with 2 and we are left with r upon r radian. And so the answer of first part is ton 15. Let us now proceed on to the second part where we are given the length of the arc equal to 15 cm. Now again since theta degrees is equal to r upon r radian and here length of the arc we have denoted as capital R. Therefore theta degrees r upon small r which is the length of the pendulum radian when substituting the values we have 15 upon 75 radian which is equal to 15 pi is the 75, 15 into 1 is pi bar 15. So 1 upon 5 ring. This answer of the sigma arc is 1 upon 5. Let us now proceed on to the third part where we are given length of arc is equal to 21 cm. Now since theta degree is equal to capital R upon small r radian the capital R we have denoted as the length of the arc and small r is the length of the pendulum. So we have 21 upon 75 radian and now since 3 is the common factor of the numerator and denominator. So we have 3 7s at 21, 3 into 25 is 75 so we have 7 upon 25 radian. The solution of the third part is 7 upon 25. Remember that when a pendulum swings it makes a circle and we are considering here the length of the arc which we have denoted by capital R which in 3 cases are 10 cm, 15 cm and 21 cm respectively. This is the point O and this is the length of the pendulum which is 75 cm. So to find the length of the arc which we have denoted by capital R we will apply the formula of length of an arc of a circle. So this completes the solution. Hope you enjoyed it. Take care and bye for now.