A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to
`v(x) = beta x^(-2 n)`
where `beta` and `n` are constant and `x` is the position of the particle. The acceleration of the particle as a function of `x` is given by.

Options

A. `-2n beta^(2)x^(-2n-1)`
B. `-2n beta^(2)x^(-4n-1)`
C. `-2beta^(2) x^(-2n+1)`
D. `-2n beta^(2)x^(-4n+1)`

Answer

B

Explanation

Given, `upsilon=beta x^(-2n)`
`a=(d upsilon)/(dt)=(dx)/(dt).(d upsilon)/(dx)`
`rArr a=upsilon(d upsilon)/(dx)=(beta x^(-2n))(-2n beta x^(-2n-1))`
`rArr a=-2n beta^(2)x^(-4n-1)`