Question

A square brass plate of side 1.0m and thickness 0.005m is subjected to a force F on its smaller opposite edges causing a displacement of 0.02 cm. If the shear modulus of brass is $0.4\times {10}^{11}N/m^2$ the value of the force F is

• A. $0.4\times {10}^{3}N$
• B. 400 N
• C. $0.4\times {10}^{4}N$
• D. 1000 N

Answer 1

The correct option is C $0.4\times {10}^{4}N$

Shear modulus,

$\eta =\frac{\frac{F}{A}}{\frac{△l}{l}}$

$\therefore =\eta \times \frac{△l}{l}\times A$

Here,

$\eta =0.4\times {10}^{11}N/m^2$

$△l=0.02cm=\frac{0.02}{100}m$

$l=1.0m$

$A=l\times t$

$=(1.0\times 0.005)m^2$

Putting these values we get,

$F=0.4\times {10}^{11}\times \frac{0.02}{100\times 1}\times (1.0\times 0.005)$

$=0.4\times {10}^{4}N$