A bob in tied to a string of length l & and kept on a horizontal rough surface as shown in the figure when point O of the string is fixed. The bob is given a tangential velocity `V_(0)` keeping the string taut as shown in figure. Find the tension in the string as a function of time. The coefficient of kinetic friction is `mu`.

Options

A. (a)`m (v_(0) - mu g t)^(2) //1`
B. (b)`m (v_(0) + mu g t)^(2) //1`
C. (c)`m (v_(0) + gt)^(2) //1`
D. (d)`m(v_(0) - gt)^(2)//1`

Answer

A

Explanation

Kinetic friction acting `= mu m g`
(Tangential retardation) = - `mu g`
Velocity at any time `V = V_(0) - mu g t`
Tension is string `= T = (m v^(2))/(l)` {as it will be in a circular motion)
`= (m (v_(0) - mu gt)^(2))/(l) T = (m (V_(0) - mu g t)^(2))/(l)`