Question

Find frequency of 2 blocks performing shm under electric field

Answer 1

In equilibrium position weight of cylindrical block is equal to force of buoyancy by liquid.force of buoyancy is equal to weight of liquid displaced.weight of block=area of cross section×length×density×acceleration due to gravityweight of block=A×l×ρ×g force of buoyancy=volume of block in liquid×density of liquid×acceleration due to gravity=A×X×3ρ×g (X is length of block in liquid)in equilibriumA×l×ρ×g=A×X×3ρ×g60cm=3XX=20cmlet block is displaced by x from equilibrium position net force acting on it isF=A×l×ρ×g-A(x+X)×3ρ×g=-A×3ρ×g×xmass×acceleration=-A×3ρ×g×xA×60×ρ×a=-A×3ρ×g×x (a is acceleration)a=-3×g60xa=ω2×xω=3×10.6=50=52T=2π5Length of cylinder inside liquid is 20 cm and block willperform shm till it is lying in liquid so it can oscillate with maximum amplitude when its lower surfacecomes upto the upper level of water.so its maximum amplitude is 20cm