Question 166: Properties of Matter

Question

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

Accepted Answer

$${F \over A} = y.{{\Delta \ell } \over \ell }$$
$$\Delta \ell  \propto F$$         . . .. (i)
T $$=$$ mg
T $$=$$ mg $$-$$ f
B
$$=$$ mg $$-$$ $${m \over {{\rho _b}}}.{\rho _\ell }.$$g
$$ = \left( {1 - {{{\rho _\ell }} \over {{\rho _b}}}} \right)$$ mg
$$ = \left( {1 - {2 \over 8}} \right)$$ mg
T' $$=$$ $${3 \over 4}$$ mg
From   (i)
$${{\Delta \ell '} \over {\Delta \ell }} = {{T'} \over T} = {3 \over 4}$$
$$\Delta \ell ' = {3 \over 4}.\Delta \ell  = 3$$ mm

Answer

5.0 mm

Answer

zero

Answer

3.0 mm

Answer

4.0 mm

Properties of Matter

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