 Hello and welcome to the session the question says, a body of mass 10 kg hangs by a string from a fixed point. The string is drawn out of the vertical by applying a force of 49 newtons to the body in which direction should this force be applied in order that in equilibrium the deflection of the string from the vertical may be of 30 degrees. Also find the tension in the string. Let's start with the solution. So here we are given that a body of mass 10 kg. So we are given that mass of the body is 10 kgs which is equal to 10 into 9.8 newtons or this is for the equal to 98 newtons. So in this figure let O A beta string such that the end A is of weight 98 newtons or 10 kg. Suppose the force of 49 newtons is applied to the weight in the direction making an angle alpha to the vertical. So in equilibrium position the deflection of the string as we are given is of 30 degrees. Then the weight free is an equilibrium under the three forces. That is the weight of 98 newtons acting vertically downwards, tension in the string O P and a force of 49 newtons. So let's see this once again. We have let O A beta string such that the end A has a weight of 98 newtons. Suppose the force of 49 newtons is applied to the weight in the direction making an angle alpha to the vertical in the equilibrium position the deflection of the string is 30 degrees. Then the weight at P is an equilibrium under the three forces. First is weight of 98 newtons acting vertically downwards, tension T in the string O P and a force of 49 newtons. Therefore by Lamb's theorem we have 98 divided by the angle opposite to it which is sin of alpha plus 30 degrees is equal to 49 divided by this angle which is sin of 180 degrees minus 30 degrees is equal to tension T and its opposite angle which is sin of 180 degrees minus alpha or this can further be written as 98 divided by sin alpha plus 30 degrees is equal to 49 divided by sin pi minus theta sin theta. So here we have sin 30 degrees is equal to T divided by sin alpha sense again sin pi minus alpha and sin alpha. Now on comparing the first to we get sin 30 degrees is equal to 49 divided by 98 into sin of alpha plus 30 degrees. Now sin 30 degrees half is equal to on simplifying this here also we have half into sin of alpha plus 30 degrees this implies that sin alpha plus 30 degrees is equal to 1 and we know that sin 90 degrees is equal to 1 therefore we have alpha plus 30 degrees is equal to 90 degrees which imply that alpha is equal to 60 degrees. So this angle is of measure 60 degrees. Now again by this we have 98 divided by sin alpha plus 30 degrees that is 90 degrees is equal to T divided by sin alpha that is sin 60 degrees or we have T is equal to 98 into sin 60 divided by sin 90 degrees is equal to 98 into root 3 divided by 2 or we have T is equal to on simplifying 49 root 3 Newton's hence the answer is tension in the string is 49 root 3 Newton's. So this completes the session by and take care.