What will be needed in order to restore the balance if necessary?

You have a beam balance, the kind of scales that tips from one side to the other, depending on the weight on each side. On the left side lies a kilogram of ice. On the right side lies the standard kilogram. The pans are in balance.
After a while all the ice melted.
Does the balance tip to the right, to the left, or does it remain unchanged?
What will be needed in order to restore the balance if necessary?

The force required to hold a water hose

Calculate the force required to hold a water hose of radius 0.04 m when it emits a jet of water at a speed of 20 m/s.

The stones in the container

A vertical container (right rectangular prism) with base area measuring 0.15 m by 0.2 m is being filled with identical small stones, each with a volume of 2*10-8 m3 and a mass of 0.05*10-3 kg. Assume that the volume of the empty spaces between the stones is negligible. If the height of the stones in the container increases at the rate of 3*10-3 m/s, at what rate does the mass of the stones in the container increase?

A yacht drops anchor

A yacht drops its anchor overboard. What happens to the water
level?

A ball fell into a vessel

A wooden ball fell into a high cylindrical vessel. The diameter of the vessel and the diameter of the ball is 5 cm and 4 cm respectively. Can you get the ball without touching the vessel?

Which of the following is a mixture?

Which of the following is a mixture?
a) water
b) carbon-dioxide
c) methane
d) coffee with milk
e) air
f) salt
g) brass
h) sugar
i) mayonnaise
j) none of the above
k) all of the above

What is the density of the material from which the object is made?

In the vessel are two immiscible liquids with densities ρ1 and ρ2 and layers of thickness h1 and h2 respectively. From the surface of liquid is lowered a streamlined object which reaches the bottom right at the moment when its speed becomes zero. What is the density of the material from which the object is made?