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Question

In the given figure a block of mass M and density ρ is immersed in liquid of density σ. The block is attached to the spring from top and string from bottom. Elongation in the spring when string is tight is x and spring constant is Mg3x.

 Column 1 Column 2 Column 3   (Tension developed in string) (Force generated in spring)(I)If ρ=2g/cc(i)T=4Mg3(P)F=Mg3 σ=1g/cc    (II)If ρ=1g/cc(ii)T=Mg3(Q)F=0 σ=1g/cc    (III)If ρ=1g/cc(iii)T=Mg2(R)F=Mg2 σ=2g/cc    (IV)If ρ=1.2g/cc(iv)T=0(R)F=4Mg3 σ=0.8g/cc    
Which of the following is true for ρ>σ?
  1. (I) (iv) (S)
  2. (IV) (ii) (P)
  3. (IV) (ii) (S)
  4. (I) (iv) (R)


Solution

The correct option is D (I) (iv) (R)
ρ=2g/ccσ=1g/ccWapp=Mg(1σρ)=Mg2

Due to this elongation in spring is
kx=Mg2Mg3xx=Mg2x=3x2 T=0and F=Mg2
II. Wapp=0T=F=Mg3x.x=Mg3
III. x' = x
  F=Mg3x.x=Mg3T=Mg3+Mg=43Mg

IV.  Wapp=Mg(1σρ)
=Mg3F=Mg3
T = 0

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