A cradle is ‘h’ meters above the ground at the lowest position and ‘H’ meters when it is at the highest point…

Q: A cradle is ‘h’ meters above the ground at the lowest position and ‘H’ meters when it is at the highest point. If ‘v’ is the maximum speed of the swing of total mass ‘m’ the relation between ‘h’ and ‘H’ is

(a) $ \displaystyle \frac{1}{2}mv^2 + h = H $

(b) $ \displaystyle \frac{v^2}{2 g} + h = H $

(c)$ \displaystyle \frac{v^2}{ g} + 2h = H $

(d) $ \displaystyle \frac{v^2}{2 g} + H = h $

Ans: (b)

$ \displaystyle m g H = m g h + \frac{1}{2} m v^2 $

$ \displaystyle g ( H – h ) = \frac{1}{2} v^2 $

$ \displaystyle ( H – h ) = \frac{v^2}{2 g} $

$ \displaystyle H = \frac{v^2}{2 g} + h $