An initially empty beaker, in the shape of a cylinder with cross sectional area A, is left out in th rain. The raindrops hit the beaker vertically downward with speed v. The rain continues at a constant rate, so the height of the water in the beaker h(t) increases with time t at a rate dh/dt=u, where u is small compared to v. The raindrops quickly come to rest inside the beaker, so we can neglect any kinetic energy of the water that has collected in the beaker. Let p denote the density of water (i.e., the mass per unit volume)

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An initially empty beaker, in the shape of a cylinder with cross sectional area A, is left out in th rain. The raindrops hit the beaker vertically downward with speed v. The rain continues at a constant rate, so the height of the water in the beaker h(t) increases with time t at a rate dh/dt=u, where u is small compared to v. The raindrops quickly come to rest inside the beaker, so we can neglect any kinetic energy of the water that has collected in the beaker. Let p denote the density of water (i.e., the mass per unit volume) Ley y_(cm)(t) denote the height of the centre of mass of all the water that has collected in the beaker by time t. what is the rate at which this height increaes (i.e. dy_((cm)//dt) ?

Is there any difference in the rate of reaction in the two beakers ?

A glass beaker of mass 400 kg floats in water with the open end just touching the surface of water and half of the beaker filled with water. The inner volume of the beaker is 500 cm^3 What is the density of the meterial of the beaker ?

A beaker is 3/7 th filled with water. Another 16 L of water is needed to fill the beaker to its brim. What is the capacity of the beaker?

A train accelerates from at the constant rate b for time t_(2) at a constant rate a and then it retards at the comes to rest. Find the ratio t_(1) // t_(2) .

If a beaker holds 576g of water, what will be the gram molecules of water in that beaker ?

A piece of ice, with a stone frozen inside it , is floating in water contained in a beaker. What will be the position of level of water in the beaker if the whole ice melts?