Advertisement Remove all ads

# Two Wires a and B Are Made of Same Material. the Wire a Has a Length L and Diameter Rwhile the Wire B Has a Length 2l and Diameter R/2. - Physics

MCQ

Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is

#### Options

• 1/8

• 1/4

• 4

• 8

Advertisement Remove all ads

#### Solution

$\text{ Let the Young's modulus of the wire's material be Y .}$

$\text{ Here: }$

$\text{ Force = F }$

$A_1 = \pi r^2$

$L_1 = l$

$A_2 = \pi \left( \frac{r}{2} \right)^2 = \frac{\pi r^2}{4}$

$\text{ L }_2 = 2\text{l }$

$\text{ Let the elongation in A be x and that in B be y }.$

$\text{ Since the Young's modulus for both the wires is the same: }$

$Y = \frac{\frac{F}{A_1}}{\frac{x}{l}} = \frac{\frac{F}{A_2}}{\frac{y}{2l}}$

$\Rightarrow \frac{x}{y} = \frac{A_2}{2 A_1}$

$\Rightarrow \frac{x}{y} = \frac{1}{8}$

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 14 Some Mechanical Properties of Matter
MCQ | Q 4 | Page 298
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?