A 6000 kg rocket is set for vertical firing. If the exhaust speed is 1000 m s⁻¹, the amount of gas that must be ejected per second to supply the thrust needed to overcome the weight of the rocket is 10x kg. The value of x is .... (g = 10 m s⁻²).
Physics · Mixed Chapter
JEE Mains

Question

A 6000 kg rocket is set for vertical firing. If the exhaust speed is 1000 m s⁻¹, the amount of gas that must be ejected per second to supply the thrust needed to overcome the weight of the rocket is 10x kg. The value of x is .... (g = 10 m s⁻²).

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Rocket thrust is F=Ṁu where Ṁ is exhaust mass rate and u the relative exhaust speed. Step 2: To balance the initial rocket weight, Ṁ(1000)=(6000)(10). Step 3: Ṁ=60 kg/s. The question writes the rate as 10x kg per second; 10x=60, so x=6.