A thin uniform rod of length L is resting against a wall and the floor as shown in the figure. Its lower end A is pulled towards left with a constant velocity v . Then the downward velocity v^ of the other end B when the rod makes an angle with the floor is

Step-by-step solution

According to the question, Given, length of the uniform rod =L the angle between rod and floor = the angle between wall and floor =90^ Let the distance between point O to A is x and the distance between point O to B is y . Now, By the velocity displacement relation w.r.t t (- negative sign denoted that y is decreasing.) Futher, x^2+y^2=L^2 [From the figure] Differentiating above equation w.r.t., time t , 2 x d x d t +2 y d y d x =0 Now, putting the values of d x d t and d y d t from Eqs. (i) and (ii), we get x v=y