A cuboid block is floating in a liquid with half of its volume immersed in the liquid.When the whole system accelerates upwards with an acceleration of g/3 . The fraction of volume immersed in the liquid will be a)1/2 b)3/8 c)2/3 d)3/4 please help


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Question Number 52273 by Necxx last updated on 05/Jan/19
$A cuboid block is floating in a liquid with half of its volume immersed in the liquid.When the whole system accelerates upwards with an acceleration of g/3 . The fraction of volume immersed in the liquid will be a)1/2 b)3/8 c)2/3 d)3/4 please help$
$A c u b o i d b l o c k i s f l o a t i n g i n a$ $l i q u i d w i t h h a l f o f i t s v o l u m e$ $i m m e r s e d i n t h e l i q u i d . W h e n t h e$ $w h o l e s y s t e m a c c e l e r a t e s u p w a r d s$ $w i t h a n a c c e l e r a t i o n o f g / 3 . T h e$ $f r a c t i o n o f v o l u m e i m m e r s e d i n$ $t h e l i q u i d w i l l b e$ $a) 1 / 2 b) 3 / 8 c) 2 / 3 d) 3 / 4$ $p l e a s e h e l p$
	Answered by mr W last updated on 05/Jan/19
	$ρ=density of block ρ_w =density of liquid w=fraction of volume immersed let′s say the volume of block is 1. (1) w=0.5 ρg=wρ_w g=0.5ρ_w g ⇒ρ_w =2ρ (2) w=? wρ_w g−ρg=ρa=ρ(g/3) ⇒w=((4ρ)/(3ρ_w ))=((4ρ)/(3×2ρ))=(2/3) ⇒answer c$
	$ρ = d e n s i t y o f b l o c k$ $ρ_{w} = d e n s i t y o f l i q u i d$ $w = f r a c t i o n o f v o l u m e i m m e r s e d$ ${l e t}^{'} s s a y t h e v o l u m e o f b l o c k i s 1 .$ $(1) w = 0.5$ $ρ g = w ρ_{w} g = 0.5 ρ_{w} g$ $\Rightarrow ρ_{w} = 2 ρ$ $(2) w = ?$ $w ρ_{w} g - ρ g = ρ a = ρ \frac{g}{3}$ $\Rightarrow w = \frac{4 ρ}{3 ρ_{w}} = \frac{4 ρ}{3 \times 2 ρ} = \frac{2}{3}$ $\Rightarrow a n s w e r c$
	Commented by mr W last updated on 05/Jan/19

	${i t}^{'} s a l a n g u a g e t r a p!$ $i f i t i s m e a n t w i t h ‘ ‘ t h e w h o l e {s y s t e m}^{″} t h e$ $b l o c k a n d t h e l i q u i d t o g e t h e r, t h e n$ $t h e a n s w e r (a) i s c o r r e c t . b u t i, m a y b e$ $t h e m o s t o f o t h e r p e o p l e u n d e r s t a n d$ $t h a t t h e t a n k i s m e a n t, t h e n a n s w e r$ $(c) i s c o r r e c t . s o t h i s i s n o t a g o o d$ $q u e s t i o n . a g o o d q u e s t i o n s h o u l d l e t$ $t h e s t u d e n t s u n d e r s t a n d w h a t i s$ $e x a c t l y m e a n t w i t h t h e q u e s t i o n .$
	Commented by Necxx last updated on 05/Jan/19
	$Thank you sir but the answer in the file says answer is a. see their explanation fraction of volume immersed in the liquid .It depends on the densities of the block and liquid. So there will be no change in it if system moves upward or downwards with constant velocity or some acceleration.$
	$T h a n k y o u s i r b u t t h e a n s w e r i n t h e$ $f i l e s a y s a n s w e r i s a .$ $s e e t h e i r e x p l a n a t i o n$ $f r a c t i o n o f v o l u m e i m m e r s e d i n$ $t h e l i q u i d . I t d e p e n d s o n t h e$ $d e n s i t i e s o f t h e b l o c k a n d l i q u i d .$ $S o t h e r e w i l l b e n o c h a n g e i n i t i f$ $s y s t e m m o v e s u p w a r d o r d o w n w a r d s$ $w i t h c o n s t a n t v e l o c i t y o r s o m e$ $a c c e l e r a t i o n .$
	Commented by Necxx last updated on 05/Jan/19

	$w o w . . . . . T h a n k s a l o t . I t s c l e a r n o w$
	Commented by mr W last updated on 06/Jan/19

	$w e c a n i m a g e t h e b l o c k i s f l o a t i n g i n$ $w a t e r i n a t a n k w h i c h i s p l a c e d i n a$ $l i f t . w h e n t h e l i f t (t a n k) (t h i s i s w h a t w e$ $u s u a l l y u n d e r s t a n d a s t h e w h o l e s y s t e m)$ $m o v e s u p w a r d s w i t h a n a c c e l e r a t i o n$ $g / 3, w e k n o w t h e b l o c k w i l l i m m e r s e$ $m o r e i n t o t h e w a t e r t h a n b e f o r e .$ $b u t t h e q u e s t i o n e r m e a n s t h e b l o c k$ $w i l l a l s o b e g i v e n t h e s a m e a c c e l e r a t i o n$ $a s t h e t a n k . t h i s i s o n l y t h e c a s e w h e n$ $t h e b l o c k {d o e s n}^{'} t f l o a t f r e e l y i n w a t e r,$ $b u t i s t i g h t l y c o n n e c t e d w i t h t h e t a n k .$ $w h e n t h e b l o c k i s t i g h t l y f i x e d w i t h$ $t h e t a n k, t h e b l o c k c a n c e r t a i n l y n o t$ $i m m e r s e m o r e o r l e s s i n t o t h e w a t e r .$ $s o a g a i n, t h e q u e s t i o n (b e t t e r t o s a y$ $t h e a n s w e r g i v e n) i s n o t g o o d, {i t}^{'} s$ $n o t f r o m t h i s w o r l d .$
	Commented by peter frank last updated on 06/Jan/19

	$p e r f e c t$
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