Question

Trolley A, moving towards the right, collides with stationary trolley B. They stick together, and move off at less than half A's original speed. Which has the greater mass, A or B?​

Answer 1

Answer:

Trolleys has greater mass than Trolley B

Answer 2

B has greater mass.

Explanation:

$let \: mass \: of \: A \: be \: m_{1} \: and \:B \: be \: m_{2} \\let \: initial \: velocity \: of \: A \: be \: u_{1} \: and \: B \: be \: u_{2}\\let \: combined \: final \: velocity \: of \: A \: and \: B \: be \: v \\ by \: law \: of \: conservation \: of \:linear \: momentum \\ m_{1}u _{1}+ m_{2}u_{2} = m_{1}v_{1}+ m_{2}v_{2} \\ here \: u _{2} = 0 \: and \: \:v_{1} = v_{2} = v\\ m_{1}u _{1}+ m_{2} \times 0 =v(m_{1}+ m_{2} ) \\ m_{1}u _{1} =v(m_{1}+ m_{2})\\ \frac{u _{1}}{v} = \frac{m_{1}+ m_{2}}{m_{1}} \\ \frac{u _{1}}{v} = \frac{m_{2}}{m_{1}} + 1 \\ here \: v < \frac{u _{1}}{2} \\2v < u _{1} \\ 2 < \frac{u _{1}}{v} \\ so \: \frac{m_{2}}{m_{1}} + 1 > 2 \\ \frac{m_{2}}{m_{1}}> 1 \\ m_{2} > m_{1}$