Question

Two spheres of volume 250 cc each but relative density is 0.8 and 1.2 connected by a light string and the combination is immersed freely in water as shown in the figure

Answer 1

your question is incomplete. A complete question is ----> Two spheres of volume 250 cc each but relative density is 0.8 and 1.2 connected by a light string and the combination is immersed freely in water as shown in the figure, tension in string is ...

solution : we know, heavier sphere will be down and lighter sphere will be up. [ see figure ]

so tension on heavier sphere will be upward.

Let the density of liquid be $\rho$

density of heavier sphere = 1.2 × 1000 kg/m³ = 1200 kg/m³

density of lighter sphere = 0.8 × 1000 = 800 kg/m³

for heavier sphere,

$(250cc\times1200\times g)-T=250cc\rho g$

or, $(250\times10^-6\times1200\timesg)-T=250\times10^-6\rho g$......(1)

for lighter sphere,

$(250cc\times800\times g)+T=250cc\rho g$

or, $250\times10^-6\times800\times g)+T=250\times10^-6\rho g$......(2)

from equations (1) and (2),

2T = 250\times10^-6\times(1200-800)g[/tex]

= 250 × 10^-6 × 400 × 10

= 1000000 × 10^-6

= 1N

hence, T = 0.5 N