A 20 ~g copper block is suspended by a vertical spring causing 1 ~cm elongation over the natural length of spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper 9000 ~kg ~m ⁻³ , Density of water 1000 kg m ⁻³, ~g =10 ~ms ⁻² )

Step-by-step solution

Mass of Block, m =20 ~g =20 10⁻³ ~kg Elongation, x=1 ~cm =0.01 ~m Spring elongation after immersed in water, x ^ = ? Density, =9000 ~kg / m ^3 Density of water, _ =1000 ~kg / m ^3 At equilibrium, kx = mg k = mg x = 0.002 10 0.01 =2 ~N / m when mass is immersed in water aligned & mg = kx ^ + ( _ V ) g & mg = kx ^ + _ [ m _ c ] g & 20 10⁻³ 10=2 x ^ + 1000 9000 20 10⁻³ 10 & 0.2=2 x ^ + 1 9 0.2 & 0.1 10 = x ^ + 1 90 & x ^ = 1 10 - 1 90 =0.89 & x ^ =0.89 aligned