A rocket of mass 4000, kg is set for vertical | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The upward thrust force $F_T$ exerted by the ejected gas is given by $F_T = v_{rel} \cdot \frac{dm}{dt}$,where $v_{rel} = 980\, m/s$ is the exhaus

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(C) The upward thrust force $F_T$ exerted by the ejected gas is given by $F_T = v_{rel} \cdot \frac{dm}{dt}$,where $v_{rel} = 980\, m/s$ is the exhaust speed and $\frac{dm}{dt}$ is the rate of mass ejection.According to Newton's second law for the rocket,the net force is $F_{net} = F_T - mg = ma$.Substituting the given values: $980 \cdot \frac{dm}{dt} - 4000 	imes 9.8 = 4000 	imes 19.6$.$980 \cdot \frac{dm}{dt} = 4000 	imes 19.6 + 4000 	imes 9.8$.$980 \cdot \frac{dm}{dt} = 4000 	imes (19.6 + 9.8) = 4000 	imes 29.4$.$\frac{dm}{dt} = \frac{4000 	imes 29.4}{980} = 4000 	imes 0.03 = 120\, kg/s$.Therefore,the gas must be ejected at a rate of $120\, kg/s$.

$A$ rocket of mass $4000\, kg$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have an initial upward acceleration of magnitude $19.6\, m/s^2$? [Exhaust speed of fuel $= 980\, m/s$.]

Similar Questions

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

Bullets of mass $50 \, g$ are fired from a gun of mass $10 \, kg$ with a velocity of $300 \, m/s$. If $5$ bullets are fired per second,then what force must a person apply on the gun so that it does not recoil? $(N)$

$A$ balloon has $2 \,g$ of air. $A$ small hole is pierced into it. The air comes out with a velocity of $4 \,m/s$. If the balloon shrinks completely in $2.5 \,s$,the average force acting on the balloon is ..........$N$.

$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

$A$ spaceship in space sweeps stationary interplanetary dust. As a result,its mass increases at a rate $\frac{dM(t)}{dt} = bv^2(t)$,where $v(t)$ is its instantaneous velocity. The instantaneous acceleration of the spaceship is

Vedclass Test Series

Exam Paper Generator

Online Exam Module