Question

How much work is done in raising a stone of mass 5 kg and relative density 3 lying at the bed of a lake through height of 3 meter? (Take $g=10m{s}^{-2}$):

• A. 25 J
• B. 100 J
• C. 75 J
• D. none

Answer 1

The correct option is C 75 J

$netforce=W-boyancy$

ds , dw are dencity of stone & water respectively & V is volume of stone then ,

$boyancy=d_w{V}_g$

$W=mg=d_s{V}_g$

$F_{n}et=V_g(d_s-d_w)$

$F_{n}et=ma=d_s{V}_g$

$a=g(1-d_w/d_s)$

$relative-density=d_s/d_w=2$ (given)

so ,$a=g/2$

now work is done against this force

$work=maX$ (X displacement)

$=5\ast \left(g/2\right)3=75j$