Question

A conical container of radius R= 1m and height H = 5m is filled completely with liquid. There is a hole at the bottom of container of area π × 10–3 m2 (see figure). Time taken to empty the conical container (in sec) is 100T. Find the value of T.

Answer 1

Explanation:

Given that, A conical container of base radius 'r' and height 'h' is full of water which is poured into a cylindrical container of radius r

Volume of water =volume of conical flask =

3

1

πr

2

h

Now, the water is poured into cylindrical flask.

Volume of cylinder =volume of water

=π(mr)

2

×hieght=

3

1

×r

2

h

Height =

3m

2

h

cm

Answer 2

2.02 is the value of T. Hence time taken to empty the conical container is $202s$

Explanation:

Radius of the conical container $,R=1m$

Height  of the conical container $,H=5m$

Area of the hole at the bottom of the container $\[=\pi \times {{10}^{-3}}{{m}^{2}}\]$

Time is taken to empty the conical the container$=100T$

Formula to find Time Taken to empty the conical container,

$\[t=\frac{2}{5}\frac{{{H}^{\frac{5}{2}}}}{{{r}^{2}}\sqrt{2g}}{{(\tan \theta )}^{2}}\]$

where $g=9.8$

$\[\tan \theta =\frac{R}{H}=\frac{1}{5}\]$

r is the radius of the hole

to find r,

$\[\pi {{r}^{2}}=\pi {{10}^{-3}}\]$

Therefore, $r^{2} =10}^{-3}$

Substitute all the values in the equation,

$\[t=\frac{2}{5}\frac{{{5}^{\frac{5}{2}}}}{{{10}^{-3}}\sqrt{2\times\9.8 }}{(\frac{1}{5})^{2}$

$t=202s$

from the question, Time taken to empty the conical container is 100T.

equate both the time taken value,

$100T=202$

$T=2.02$