Variable Mass System||Rocket Propulsion||Wagon with Leakage||Wagon in Rain||Contain having Leakage on Vartical Surface

Variable Mass|Rocket Propulsion|Questions

To illustrate th principle of a rocket, a student designed a water rocket as shwon in the figure. It is basically a container having pressurized gas in its upper part and water in its lower part. Pressure of the gas is 4.0Mpa. Mass of empty container is 1.0kg and mass of its content is also 1.0kg. The nozzle at the bottom is opened to impart a vertical acceleration to the contaienr. If it is desired that the initial upwards acceleration of the container be 0.5g. what should be the cross sectional area (A) of the exit of the nozzle? Neglect the pressure due to height of water in the contaienr and take atmospheric pressure to be 1.0MPa. g= 10ms^(-2) .

A vessel of volume V contains an ideal gas at absolute temperature T and pressure P. The gas is allowed to leak till its pressure falls to P'. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

Two containers of sand are arranged like the block as shown in fig. the containers alone have negligible mass, the sand in them has a total mass M_("tot") , the sand in the hanging container H hs mass m. To measure the magnitude a of the acceleration of the system, a large number of experiments carried out where m varies from experiment to experiment but M_("tot") does not, that is, sand in shifted between the containers before each trial . Which of them gives the tension in the connecting cord (vertical axis is for tension) ?

Two containers of sand are arranged like the block as shown in fig. the containers alone have negligible mass, the sand in them has a total mass M_("tot") , the sand in the hanging container H hs mass m. To measure the magnitude a of the acceleration of the system, a large number of experiments carried out where m varies from experiment to experiment but M_("tot") does not, that is, sand in shifted between the containers before each trial . Which of the curves in graph correctly gives acceleration magnitude as a function of the ratio m//M_("tot") (vertical axis is for acceleration)?