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A spherical ball of radius r and relative density 0.5 is floating in equilibrium in water with half of it immersed in water.The work done in pushing the ball down so that the whole of it is immersed in water is(d=density of water)
choose:
(a)5/12(3.14*r4dg) (b)2/3(3.14*r4dg)
and please tell how?
answer is b
this is bcuz when it will be immersed buoyancy= 4/33.14*r3.and weight acting downward =2/3*3.14 *r3and external force is f
,by this f= 2/3 *3.14*r3. and work done = b option
Energy conservation applying –
K.Ei + P.Ei = K.Ef + P.Ef
0 + mgi – Buoyant forcei = 0 + mgf – Buoyant forcef + W.D
[0.5 x 4/3 x 3.14 x r3 x g].r – [d x 2/3 x 3.14 x r3 x g].r =
[0.5 x 4/3 x 3.14 x r3 x g].r – [d x 4/3 x 3.14 x r3 x g].r+ W.D
[d x 4/3 x 3.14 x r3 x g].r -[d x 2/3 x 3.14 x r3 x g].r = W.D
W.D = 2/3(3.14*r4dg)
B should be the answer.
THIS CAN BE DONE BY ENERGY CONSERVATION ...
BY APLLYING E- CONSERVATION WE CAN CALCULATE IT.
SO YOUR ANSWER WILL BE ---- (b)
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