A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take`g=10ms^(-2)`)

Options

A. `2pisqrt(2)s`
B. `2s`
C. `2sqrt(2)s`
D. `sqrt(2)s`

Answer

C

Explanation

A uniform string of length 20 m is suspended from a rigid support. Such that the time taken to reach the support,
`T=(mgx)/(1)`
So, velocity at point `p=sqrt(((mgx)/(1))/(m//1))`
i.e `V= sqrt(gx),` `(dx)/(dt)=sqrt(gx)`
`rArr int_(0)^(20)(dx)/(sqrtX)=int_(0)^(t)sqrt(gdt)`,`[2sqrt(X)]_(0)^(20)=sqrt(10t)rArr2sqrt(20)=sqrt(10t)` `t=2sqrt(2S)`