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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    A load of mass M kg is suspended from a  steel wire  of length 2 m and radius 1.0 mm in Searle' experiment. The increase in length product wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the length of load is 8. The new value of increase in ength of the steel wire is:

    A) 3.0 mm            

    B) 4.0 mm

    C) 5.0 mm                        

    D) zero

    Correct Answer: A

    Solution :

    In first case: \[\frac{\frac{mg}{A}}{\left( \frac{\Delta {{\ell }_{1}}}{\ell } \right)}=Y\]\[\Rightarrow \] \[\Delta {{\ell }_{1}}=\frac{mg}{\left( \frac{YA}{\ell } \right)}\]
    In second case: \[\frac{\frac{mg-B}{A}}{\left( \frac{\Delta \ell }{\ell } \right)}=Y\]
    \[\Rightarrow \]   \[\Delta {{\ell }_{2}}=\frac{mg-B}{\left( \frac{YA}{\ell } \right)}=\frac{\left( \frac{3mg}{4} \right)}{\left( \frac{YA}{\ell } \right)}\]
    \[\Rightarrow \]   \[\Delta {{\ell }_{2}}=\frac{3}{4}\Delta {{\ell }_{1}}=3mm.\]


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