Question

A girl of mass $50 \, kg$ stands on a railroad car of mass $75 \, kg$ moving with velocity $20 \, m \, s^{- 1}$ . Now, the girl begins to run with a velocity of $10 \, m \, s^{- 1}$ with respect to the car in the same direction, as that of the car. The velocity of the car at this instant will be

• A. $20ms^{- 1}$
• B. $24ms^{- 1}$
• C. $16 \, m \, s^{- 1}$
• D. $18ms^{- 1}$

Answer 1

Answer: (C)

According to the law of conservation of linear momentum,
$P_{i}=P_{f}$
$\Longrightarrow \, \, \left(50 + 75\right)20=50\left(10 + v\right)+​75v$
$\Longrightarrow \, 125\times 20=50\left(10 + v\right)+75v$
$\Longrightarrow \, \, 5\times 20=2\left(10 + v\right)+3v$
$\Longrightarrow \, \, \, 100=20+2v+3v$
$\Longrightarrow \, \, 5v=80\Longrightarrow v=16 \, m \, s^{- 1}$