A thick copper rope of density 1.5 × 103 kg / m 3 and young's modulus 5 × 106 N / m 2, 8 m in length is hung from the ceiling of a room. The increase in its length due to its own weight is

Question

A thick copper rope of density 1.5 × 103 kg / m 3 and young's modulus 5 × 106 N / m 2, 8 m in length is hung from the ceiling of a room. The increase in its length due to its own weight is (A) 9.6 × 10-5 m (B) 9.6 × 10-7 m (C) 19.2 × 10-7 m (D) 9.6 × 10-2 m

Tardigrade Admin · Accepted Answer

The increase in length due to its own weight l=(L2 d g/2 Y) =((8)2 × 1.5 × 103 × 9.8/2 × 5 × 106) =9.6 × 10-2 m

Q. A thick copper rope of density $1.5 \times 1 0^{3} k g / m^{3}$ and young's modulus $5 \times 1 0^{6} N / m^{2}, 8 m$ in length is hung from the ceiling of a room. The increase in its length due to its own weight is

$9.6 \times 1 0^{- 5} m$

$9.6 \times 1 0^{- 7} m$

$19.2 \times 1 0^{- 7} m$

$9.6 \times 1 0^{- 2} m$

The increase in length due to its own weight $l = \frac{L ^{2} d g}{2 Y}$
$= \frac{( 8 ) ^{2} \times 1.5 \times 1 0 ^{3} \times 9.8}{2 \times 5 \times 1 0 ^{6}}$
$= 9.6 \times 1 0^{- 2} m$

Q. A thick copper rope of density 1.5×103kg/m3 and young's modulus 5×106N/m2,8m in length is hung from the ceiling of a room. The increase in its length due to its own weight is

9.6×10−5m

9.6×10−7m

19.2×10−7m

9.6×10−2m