From a massless string, a metallic cube of edge 3 cm is suspended and them immersed in water as shown in figure. If the density of metal is `5 xx 10^(3) kg//m^(3)` then find the tension in the string if the given system is
(a) at rest
(b) moving downwards with an acceleration of `3m//s^(2)` .
(C) moving upwards with an acceleration of `3 m//s^(2)`.

Explanation

Density of cube `(sigma)=5 xx 10^(3)"kg/m"^(3)`
Density of water `(p)=10^(3) "kg/m"^(3)`
V=Volume of cube `=3cm xx 3 cm xx 3cm`
`=27 cm^(3) =27 xx 10^(-6) m^(3)`
W=Weight of cube `="volume "xx " density" xx g=V sigma g`
Weight of water displaced =upthrust `=Vpg`
Case (i): When system is at rest

`W=T+F_(B)`
`T=W-F_(B)`
`=V sigma g-Vpg`
`=Vg(sigma-p)`
`=27 xx 10^(-6) xx 10 xx (5000-1000)`
=1.08 N
Case (ii) :System is moving downwards

Effective value of acceleration `=g.=g-a`
`T+F_(B)=W`
`T=W-F_(B)`
`=sigma Vg.-pVg.`
`=Vg. (sigma-p)`
`=V(g-a) (sigma-p)`
`=27 xx 10^(-6) (10-3) (5000-1000)`
=0.756 N
Case (iii): When system is moving upwards then g.=g+a

Effective value of `g=g.=g+a`
`T=W-F_(B)`
`=Vsigma g.-Vpg.`
`=Vg. (sigma-p)`
`=27 xx 10^(-6) xx (10+3) (5000-1000)`
=1.40 N