The area of a cross-section of a steel wire is 0.1 cm2 and Young’s modulus of steel is 2×1011 N m-2. The force required to stretch it by 0.1 % of its length is

Question

The area of a cross-section of a steel wire is 0.1 cm2 and Young’s modulus of steel is 2×1011 N m-2. The force required to stretch it by 0.1 % of its length is (A) 1000 N (B) 2000 N (C) 4000 N (D) 5000 N

Tardigrade Admin · Accepted Answer

Here, A=0.1 cm2 =0.1×10-4 m2, Y=2×1011 N m-2 (Δ L/L)=0.1 % =(0.1/100) =0.1×10-2 As Y=(F /A/Δ L/ L) ∴ F=Y (Δ L/L)A =2×1011 N m-2×0.1×10-2×0.1×10-4 m2 =2×103 N =2000 N

Q. The area of a cross-section of a steel wire is $0.1 c m^{2}$ and Young’s modulus of steel is $2 \times 1 0^{11} N$ $m^{- 2}$ . The force required to stretch it by $0.1$ of its length is

$1000 N$

$2000 N$

$4000 N$

$5000 N$

Q. The area of a cross-section of a steel wire is 0.1cm2 and Young’s modulus of steel is 2×1011N m−2. The force required to stretch it by 0.1 of its length is

1000N

2000N

4000N

5000N

Here, A=0.1cm2 =0.1×10−4 m2, Y=2×1011Nm−2 LΔL​=0.1% =1000.1​ =0.1×10−2 As Y=ΔL/LF/A​ ∴ F=Y LΔL​A =2×1011Nm−2×0.1×10−2×0.1×10−4m2 =2×103N =2000N

Q. The area of a cross-section of a steel wire is $0.1 c m^{2}$ and Young’s modulus of steel is $2 \times 1 0^{11} N$ $m^{- 2}$ . The force required to stretch it by $0.1$ of its length is

$1000 N$

$2000 N$

$4000 N$

$5000 N$