The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm 2, is 2 × 1011 N / m 2. The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is (1/4) of its value on the earth. The elongation of wire is (Take g on the earth =10 m / s 2 ) :

Question

The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm 2, is 2 × 1011 N / m 2. The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is (1/4) of its value on the earth. The elongation of wire is (Take g on the earth =10 m / s 2 ) : (A) 0.1 cm (B) 1 mn (C) 1 cm (D) 0.1 mm

Tardigrade Admin · Accepted Answer

Tension (F)=m g =4 × (10/4)=10 N Δ L =( FL / AY ) =(10 × 6/3 × 10-6 × 2 × 1011) =10-4 m =0.1 mm

$0.1 c m$

$1 mn$

$1 c m$

$0.1 mm$

Tension $(F) = m g$
$= 4 \times \frac{10}{4} = 10 N$
$Δ L = \frac{F L}{A Y}$
$= \frac{10 \times 6}{3 \times 1 0 ^{- 6} \times 2 \times 1 0 ^{11}}$
$= 1 0^{- 4} m = 0.1 mm$

0.1cm

1mn

1cm

0.1mm

Tension (F)=mg =4×410​=10N ΔL=AYFL​ =3×10−6×2×101110×6​ =10−4m=0.1mm

$0.1 c m$

$1 mn$

$1 c m$

$0.1 mm$

Tension $(F) = m g$
$= 4 \times \frac{10}{4} = 10 N$
$Δ L = \frac{F L}{A Y}$
$= \frac{10 \times 6}{3 \times 1 0 ^{- 6} \times 2 \times 1 0 ^{11}}$
$= 1 0^{- 4} m = 0.1 mm$