108. Two astronauts each of mass 120 kg are travelling in a closed spaceship moving at 15 km/s in outer space. The total mass of the spaceship and its contents is 660 kg. If each astronaut reduces their mass to 90 kg through exercise, what will be the velocity of the spaceship?
(a) 12 km/s
(b) 18 km/s
(c) 15 km/s
(d) 10 km/s
Answer: (c) 15 km/s
Explanation:
1. Conservation of momentum:
No external force acts on the system ⇒ total momentum remains constant.
2. Total mass consideration:
The spaceship is a closed system. Any mass lost by astronauts remains inside the spaceship.
Hence, total mass remains \(660\) kg.
3. Apply momentum conservation:
\[
M_i v_i = M_f v_f
\]
Since \(M_i = M_f\),
\[
v_f = v_i = 15 \text{ km/s}
\]
Therefore, the spaceship continues with the same velocity 15 km/s.