Tension in a uniform string of length L varies with length uniformly. At one end A tension is `T_(0)` and at other end B it is `16T_(0)`. If mass per unit length of string is `mu`. Choose the correct options (s)

Options

A. Time taken by a pulse to move from end A and B is `(2)/(5)Lsqrt((mu)/(T_(0)))`
B. Time taken by a pulse to move from end A to end B is `(2)/(15)sqrt((muL)/(T_(0)))(sqrt(15)-1)`
C. Tension in the string as function of distance x from end A is `T=T_(0)+(15T_(0))/(L)x`
D. Tension in the string as function of distance x from end A is `T=T_(0)+(15T_(0))/(L)x`

Answer

A, C

Explanation

`V=(dx)/(dt)`
`impliesdt=(dx)/(V)`=`int_(0)^(L)(dx)/(sqrt((T_(0)+(15T_(0))/(L).x)/(mu)))`
`t=(2)/(5)sqrt((muL^(2))/(T_(0)))`