A body at temperature `theta_(0)` having Newton's cooling constant K is placed in a surrounding having temperature `T_(0)` at time t = 0. The graph of temperature of the body as a function of time t is shown in the adjacent figure. A tangent on the curve is drawn at t = 0 as shown in the figure. Find the value of `tau`.

Options

A. K
B. `(1)/(K)`
C. `K(Q_(0)-T_(0))`
D. Data insufficient

Answer

B

Explanation

`mgsintheta-f_(S)=ma_(C.M.)`
`(f_(s))R=((2)/(5)mR^(2))alpha`
`impliesf_(s)=(2)/(5)ma_(C.M)`
`implies mgsintheta=(7)/(5)ma_(C.M)implies a_(C.M)=(5)/(7)gsintheta`
For time of descent
`(1)/(2)a_(C.M)t^(2)=hcosectheta`
`t^(2)=(2h)/(a_(C.M))cosectheta`
`t^(2)=(2hxx7)/(5gsin theta)cosectheta`
`t^(2)=(14h)/(5g)(1)/(sin^(2)theta)implies t=sqrt((14h)/(5g))(1)/(sin theta)&V_(F)=(a_(C.M))t=((5)/(7)gsina)(sqrt((14h)/(5g)))(1)/(sin theta)`
`V_(F)=sqrt((5xx2gh)/(7))=sqrt((10gh)/(7))` implies Velocity does not depend or `'theta'` but time depend on `'theta'`