A particles moves along a circle of a fixed radius with a variable acceleration given by `a_(n) = kt^(n),` where k is a constant and t time. If the power 'P' delivered by all forces acting on it be plotted against time 't' on a log-log scale, the slope of the straight line obtained is 2 as shown in Figure below. The value of n is:

Options

A. 1
B. 2
C. 3
D. `-1`

Answer

`(3)`

Explanation

`a_(n) = kt^(n) Rightarrow (v_(n)^(2))/(r) = kt^(n) Rightarrow v_(n)^(2) = krt^(n)`
`power, P = ((1/2 mv_(n)^(2)))/t`
`P = (1/2 mkr t^(n))/t Rightarrow P = (1/2mkr)t^(n-1)`
`therefore P = k_(1)t^(n-1)` where `k_(1)` be a constant Applying log,`log P = (n-1) log t + log k_(1)`
As slope = (n -1) = 2
`Rightarrow n = 3`