Question

Two bodies of mass 1 kg and 3 kg have position vectors `hati + 2hatj + hatk` and `-3hati - 2hatj + hatk` respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector ______.

Options

• `hati - 2hatj + hatk`

• `-3hati - 2hatj + hatk`

• `-2hati + 2hatk`

• `-2hati - hatj + 2hatk`

Answer 1

Two bodies of mass 1 kg and 3 kg have position vectors `hati + 2hatj + hatk` and `-3hati - 2hatj + hatk` respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector `underlinebb(hati - 2hatj + hatk)`.

Explanation:

Position of COM of a mass system is given as,

`vecr_(com) = (m_1vecr_1 + m_2vecr_2)/(m_1 + m_2) = (1(hati + 2hatj + hatk) + 3(-3hati - 2hatj + hatk))/(1 + 3)`

= `-2hati - hatj + hatk`

`|vecr_{cm}| = |-2hati - hatj + hatk| = sqrt((2)^2 + (1)^2 + (1)^2) = sqrt6`

Only `hati - 2hatj + hatk` magnitude is `sqrt(1^1 + (-2)^2 + 1^2) = sqrt6`

So `hati - 2hatj + hatk` is correct.