SATHEE: Gravitation Question 217

Gravitation Question 217

Question: Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area $[A]$ and wire 2 has cross-sectional area $[3 A]$ . If the length of wire 1 increases by Ax on applying a force $[F]$ , how much force is needed to stretch wire 2 by the same amount?

Options:

A) $[F]$

B) $[4 F]$

C) $[6 F]$

D) $[9 F]$

Show Answer

Answer:

Correct Answer: D

Solution:

$[A_{1} l_{1} = A_{2} l_{2}]$

$[\Rightarrow l_{2} = \frac{A_{1} l_{1}}{A_{2}} = \frac{A \times l_{1}}{3 A}]$

$[\Rightarrow \frac{l_{1}}{l_{2}} = 3]$ $[Δ x_{1} = \frac{F_{1}}{A γ} \times l_{1}]$

$[\Rightarrow x_{2} = \frac{F_{2}}{3 A γ} \times l_{1}]$ Here $[Δ x_{1} = Δ x_{2}]$

$[\frac{F_{2}}{3 A γ} l_{2} = \frac{F_{1}}{A γ} l_{1} \Rightarrow F_{2} = 3 F_{1} \times \frac{l_{1}}{l_{2}} = 3 F_{1} \times 3 = 9 F]$

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Gravitation Question 217

Question: Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area [A] and wire 2 has cross-sectional area[3A] . If the length of wire 1 increases by Ax on applying a force [F] , how much force is needed to stretch wire 2 by the same amount?

Options:

Answer:

Solution:

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Question: Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area $[A]$ and wire 2 has cross-sectional area $[3 A]$ . If the length of wire 1 increases by Ax on applying a force $[F]$ , how much force is needed to stretch wire 2 by the same amount?