A mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is

Step-by-step solution

Angular velocity = ω Linear velocity = v Length of string = Radius = r If string is halved, r ' = r 2 Angular momentum, L = r × p where, r = radius vector and p = linear momentum = r × m v ∵ θ = 90 o = m v r As L remain constant, m v r = constant ⇒ If r ' → r 2 ' v ' = 2 v such that m v ' r ' = m 2 v × r 2 Hence, linear velocity will be 2 v.