A square aluminium (shear modulus is 25 10^ 9 ,Nm ^ -2 ) slab of … - Vidyadip

MCQ

A square aluminium (shear modulus is $25 \times 10^{9}\,Nm ^{-2}$ ) slab of side $60\,cm$ and thickness $15\,cm$ is subjected to a shearing force (on its narrow face) of $18.0 \times 10^{4}\,N$. The lower edge is riveted to the floor. The displacement of the upper edge is $.......\mu\,m$.

A
$24$
B
$12$
✓
$48$
D
$96$

✓

Answer

Correct option: C.

$48$

c
$\frac{ F }{ A }=\eta \frac{ x }{\ell} \Rightarrow \frac{ F \ell}{ An }= x$

$x =\frac{18 \times 10^{4} \times 60 \times 10^{-2}}{60 \times 10^{-2} \times 15 \times 10^{-2} \times 25 \times 10^{9}}$

$=48 \times 10^{-6}\,m =48\,\mu m$

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