Question

A cube of volume 1 cubic metres and specific gravity 2 is very slowly being lowered in to a lake with help of a massless string tied to one of its vertices A (i.e., body diagonal AB is perpendicular to surface of water).

Initially, the other opposite vertex B is just touching the surface of water and finally, vertex A is just beneath the surface of water. (Ignore change in KE of water). (g= 10ms2).

Find
(a) Work done by gravity on cube.
(b) Work done by gravity on water
(c) Work done by gravity on water + cube system.
(d) Work done by tension on cube.

Answer 1

a) By the formula of work:

$A=P*S$

where P is ponderosity of cube.

Specific gravity: $\gamma=\frac{P}{V}->P=\gamma*V$

$A=\gamma*V*S$

$S=d$, $d$ is the diagonal of cube. If $a=1 ->d=a\sqrt{\smash[b]{3}}=\sqrt{\smash[b]{3}}\approx1.7$

$A=2*1*1.7=3.4$ (J)

b) Work done by gravity of water:

$A=F_A*S$

$F_A$ is extrude Archimedes force. $F_A=\rho*g*V=1000*10*1=10000$ (N)

$A=10000*1.7=17000$ (J)

c) Work done by gravity on water + cube system:

$A=17000+3.4=17003.4$ (J)

d) Work done by tension on cube:

$A=3.4$ (J)