Question

A 100 g block of copper (p = 8900 kg/m^3) and a 100 g block of aluminum (p = 2700 kg/m^3) are connected by a massless string that runs over two massless, frictionless pulleys. The two blocks exactly balance, since they have the same mass. Now suppose the two blocks are submerged in water. What will happen? The copper block will fall, the aluminum block will rise. The aluminum block will fall, the copper block will rise. Nothing will change both blocks will rise

Answer 1

when a body is completelt immersed in a liquid then the upward thurst it gets fromt he liquid is equal to the weight of the liquid displaced by it.

Thus upward force on copper is $F_C= mg= ah\rho' g= V\rho' g$

where a and h is the area and the height of copper block. And V is the volume of the block. m is the mass of water displaced and $\rho'$ is the denisty of water

Aso, Since Volume= Mass/density

thus, $F_C= (M_c/\rho)\rho' g= 0.1\rho' g/ 8900 N$ ..

Similarly, upward force on aluminium block is, $F_A= (M_a/\rho)\rho' g= 0.1\rho' g/ 2700 N$ ( Since density of liquid remains same for both)

comparing both forces, we get that F_A > F_C

i.e. Aluminium will experience more upward thurst than copper. Hence Aluminium block will rise and copper block will fall. Hence correct option: a