Two particles of mass m and 2m have their position vectors as a function of time as `r_(1) (t) = hat I - t^(3) hat(j) +2t^(2)hat(k) and r_(2) (t) = t hat (i) -t^(3)hat(j) -t^(2) hatk` respectively (where t is the time). Which one of the following graphs represents the path of the centre of mass ?

Options

A. `|vecA|(at t = 1) = sqrt(2)`
B. `(dvecA)/(dt)(at t = 1) = hati+pi hatj+2hatk`
C. `|vecAxx(dvecA)/(dt)|(at t = 1) = sqrt(2pi^(2)+1)`
D. `vecA. (dvecA)/(dt)(at t = 1) = 4`

Answer

D

Explanation

The veloctors ……….
`vecA = t hati - sin pi t hatj + t^(2)hatk`
`vecA(t=1) = hati - sin pi t hat j + hatk`
`|vecA| = sqrt(2)`
`(dvecA)/(dt) = hati - pi cos pi t hatj + 2t hatk`
`(dvecA)/(dt) (t = 1) = (hati+pi hatj + 2hatk)`
`vecAxx(dvecA)/(dt) = (hati+hatk)`
`|vecAxx(dvecA)/(dt)|=- sqrt(2pi^(2)+1)`
`vecA.(dvecA)/(dt) = 1+2=3`