A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5 : 1 . The velocity of the bob at the highest position is ______ m s - 1 . (Take g = 10 m s - 2 )

Step-by-step solution

Let the speed of bob at lowest position be v 1 and at the highest position be v 2 . Maximum tension is at lowest position and minimum tension is at the highest position. Now, using, conservation of mechanical energy, 1 2 m v 1 2 = 1 2 m v 2 2 + m g 2 l ⇒     v 1 2 = v 2 2 + 4   g l       . . . . 1 Now, T max - m g = m v 1 2 l ⇒   T max = m g + m v 1 2 l &    T min + m g = m v 2 2 l ⇒   T min = m v 2 2 l - m g T max T min = 5 1 ⇒   &#