Question

diameter of a beaker is 7cm. mambler(some instrument)dia is 1.4cm.how many mamblers has to be put to increase the water level by 5.6cm.

Answer 1

Let us assume that mamblers are spherical in shape. This is our best guess because we have been told the diameter of a mambler is 1.4 cm (that is, the radius of a mambler is 0.7 cm) and no other information about the mamblers is given. Thus, the sphere is the only shape which can fulfill this.

Let the number of mamblers required to raise the level of water in the beaker by 5.6 cm be given by "m".

Now, from basic physics we know that an object that sinks displaces an amount of fluid equal to the object's volume.

We also know that the volume that has been displaced is:

$V_d=\pi r^2 h=\pi\times (\frac{7}{2})^2\times 5.6=68.6\pi$......Equation 1

(This is because the volume displaced is in the shape of a cylinder as the beaker is a cylinder and the height by which the water changes is h=5.6 cm)

Now, the volume of a mambler sphere is:

$V_m=\frac{4}{3}\pi r^3= \frac{4}{3}\pi (0.7)^3\approx0.4573 \pi$...Equation 2

Thus, from Equation 1 and Equation 2 and the use of the physical law already stated we get:

$m\times 0.4573\pi=68.6\pi$

$\therefore m=\frac{68.6\pi}{0.4573\pi}\approx 150$

Thus, 150 mamblers have to be put to increase the water level by 5.6cm.