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

Is the formula $\vec{F} = m\vec{a}$ valid in all circumstances? Why?

An ice block is melting at a constant rate $\left| \frac{dm}{dt} \right| = \mu$. Its initial mass is $m_0$ and it is moving with velocity $v$ on a frictionless horizontal surface. The distance travelled by it until it melts completely is:

$A$ gun of mass $10 \, kg$ fires $4$ bullets per second. The mass of each bullet is $20 \, g$ and the velocity of the bullet when it leaves the gun is $300 \, m/s$. The force required to hold the gun while firing is (in $N$)

$A$ rocket of mass $1000 \, kg$ exhausts gases at a rate of $4 \, kg/s$ with a velocity of $3000 \, m/s$. The thrust developed on the rocket is ........ $N$.

$A$ rocket which has a mass of $3.5 \times 10^4 \,kg$ is blasted upwards with an initial acceleration of $10 \,m/s^2$. The initial thrust of the blast is-

Vedclass Test Series

Exam Paper Generator

Online Exam Module