Q 11-06-139JEE MainJEE Main 2022 (27 Jun, Shift 1)Easy
Two blocks of masses $10$ kg and $30$ kg are placed on the same straight line with coordinates $(0, 0)$ cm and $(x, 0)$ cm respectively. The block of $10$ kg is moved on the same line through a distance of $6$ cm towards the other block. The distance through which the block of $30$ kg must be moved to keep the position of centre of mass of the system unchanged is
Answer: (C) $2$ cm towards the $10$ kg block
For the centre of mass to stay fixed, $m_1\Delta x_1 + m_2\Delta x_2 = 0$.
$$10(+6) + 30\,\Delta x_2 = 0 \;\Rightarrow\; \Delta x_2 = -2\ \text{cm}$$
The 30 kg block moves 2 cm in the negative $x$ direction, i.e. towards the 10 kg block.
Solution by Sreeraj P, M.Sc Physics