A steel wire is 1 m long and 1 mm 2 in area of cross-section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm ?

Question

A steel wire is 1 m long and 1 mm 2 in area of cross-section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm ? (A) 1000 N (B) 200 N (C) 400 N (D) 2000 N

Tardigrade Admin · Accepted Answer

(F L/A Y)=Δ x Since A, Y remain constant in given case We can say F L propto Δ x or (F1 L1/F2 L2)=(Δ x1/Δ x2) F1=200 N Δ x1=1 mm Δ x2=10.02 m -10 m =0.02 m =20 mm L1=1 m L2=10 m Substitute the values (200 × 1/F2 × 10)=(1 mm /20 mm ) F2=400 N

Q. A steel wire is 1m long and 1mm2 in area of cross-section. If it takes 200N to stretch this wire by 1mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10m to a length of 1002cm ?

1000 N

200 N

400 N

2000 N

AYFL​=Δx Since A,Y remain constant in given case We can say FL∝Δx or F2​L2​F1​L1​​=Δx2​Δx1​​ F1​=200N Δx1​=1mm Δx2​=10.02m−10m=0.02m=20mm L1​=1m L2​=10m Substitute the values F2​×10200×1​=20mm1mm​ F2​=400N

Q. A steel wire is $1 m$ long and $1 m m^{2}$ in area of cross-section. If it takes $200 N$ to stretch this wire by $1 mm$ , how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 m$ to a length of $1002 c m$ ?