Question

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A force of 10N acting downwards, is applied at the bottom of the block. Find the longitudinal strain in the wire. Area of cross section of the wire is $0.005c{m}^2$ and Young modulus of the metal is $2.0\times {10}^{11}N{m}^{-2}.$ Take $g=10m{s}^{-2}.$

• A. $5\times {10}^{-5}$
• B. $2\times {10}^{-3}$
• C. $3\times {10}^{-4}$
• D. None of the above

Answer 1

The correct option is C

$3\times {10}^{-4}$

The situation is described in the figure .

Weight of the block = Gravitational pull on the block = mg = 2 $\times$ 10 = 20 N

As the block is at rest, net force acting on it should be zero. So, we can write,

Total force acting downwards = Total force acting upwards

$T=20N+10N$ or, $T=30N$

Stress $=\frac{Force}{Area}=\frac{30N}{0.005c{m}^2}=6\times {10}^{7}N{m}^{-2}$

Longitudinal strain $=\frac{Stress}{Y}=\frac{6\times {10}^{7}N{m}^{-2}}{2\times {10}^{11}N{m}^{-2}}=3\times {10}^{-4}$