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Question: Two parallel and opposite forces each 5000 N are applied tangentially to the upper and lower face of...

Two parallel and opposite forces each 5000 N are applied tangentially to the upper and lower face of a cubical metal block of side 25 cm. The angle of shear is

(The shear modulus of the metal is 80 GPa)

A

10−4 rad10^{- 4}\text{ rad}

B

10−5 rad10^{- 5}\text{ rad}

C

10−6 rad10^{- 6}\text{ rad}

D

10−7 rad10^{- 7}\text{ rad}

Answer

10−6 rad10^{- 6}\text{ rad}

Explanation

Solution

: Here, F = 5000N

L=25cm=25×10−2mL = 25cm = 25 \times 10^{- 2}m

A=(25×10−2m)2=625×10−4m2A = (25 \times 10^{- 2}m)^{2} = 625 \times 10^{- 4}m^{2}

η=80GPa=80×109Pa\eta = 80GPa = 80 \times 10^{9}Pa

Angle of shear,

θ=FAη=5000625×10−4×80×109\theta = \frac{F}{A\eta} = \frac{5000}{625 \times 10^{- 4} \times 80 \times 10^{9}}

=10−6rad= 10^{- 6}rad