A Thread is passing through a hole at the centre of a frictionless table. At the upper end a block of mass 0.5 kg is tied and a block of mass 8 kg is ties at the lower end which freely hanging. The smaller mass is rotated on the table with

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A Thread is passing through a hole at the centre of a frictionless table. At the upper end a block of mass 0.5 kg is tied and a block of mass 8 kg is ties at the lower end which freely hanging. The smaller mass is rotated on the table with a constant angular velocity about the axis passing through the hole so as to balance the heavier mass. If the mass of the hanging block is changed from 8 kg to 1 kg . The fractiona

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Correct answer: 3

For circular motion of a body tied to a string on a horizontal plane m v^2 r =T here, T = mg aligned & m v₁^2 / r₁ m v₂^2 / r₂ = M₁ g M₂ g & v₁^2 r₂ v₂^2 r₁ = 8 1 ...(i) aligned Now as angular momentum is conserved about pt 0 . m v₁ r ₁=m v₂ r ₂....(ii) from (i) and (ii) r₁ r₂ =2 aligned & further ₂ ₁ = v₂ v₁ r₁ r₂ = ( r₁ r₂ )^2 & ₂ ₁ = ( 1 2 )^2= 1 4 & = ₂- ₁ ₂ = ₂ ₁ -1= 1 4 -1=- 3 4 aligned

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