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Byju's Answer

Standard XII

Physics

Young's Modulus of Elasticity

A light rod o...

Question

A light rod of length $2 m$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross section $0.1 c m^{2}$ . A weight is suspended from a certain point of the rod such that equal stress are produced in both the wires. Which of the following are correct?

The ratio of tension in the steel and brass wires is

0.5

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The load is suspended at a distance of

400 / 3 c m

from the steel wire

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Both (a) and (b) are correct

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Neither (a) nor (b) are correct

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Solution

The correct options are
A Both (a) and (b) are correct
B The ratio of tension in the steel and brass wires is $0.5$
C The load is suspended at a distance of $400 / 3 c m$ from the steel wire
$\frac{T_{1}}{0.1} = \frac{T_{2}}{0.2}$ or $\frac{T_{1}}{T_{2}} = \frac{1}{2} = 0.5$
Further, $T_{1} x = T_{2} (2 - x)$
or $\frac{T_{1}}{T_{2}} = \frac{2 - x}{x}$
Hence, $\frac{2 - x}{x} = 0.5 = \frac{1}{2}$ or $4 - 2 x = x$
or, $x = \frac{4}{3} m = \frac{400}{3} c m$ .

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Similar questions

Q. A light rod of length

2 m

is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section

0.1

{c m}^{2}

and the other of brass of cross-section

0.2 {c m}^{2}

. Along the rod at what distance a weight may be hung to produce equal stresses in both the wires.

(Y_{s t e e l} = 2 \times 10^{11} N m^{- 2}, Y_{b r a s s} = 1 \times 10^{11} N m^{- 2})

Q. A light rod of length

2 m

is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section

0.1

{c m}^{2}

and the other of brass of cross-section

0.2 {c m}^{2}

. At which distance a weight may be hung along the rod, in order to produce equal strains in both the wires?

(Y_{s t e e l} = 2 \times 10^{11} N m^{- 2}, Y_{b r a s s} = 1 \times 10^{11} N m^{- 2})

Q. A

2 m

long light metal rod

A B

is suspended from the ceiling horizontally by means of two vertical wires of equal length, tied to its ends. One wire is of brass and has cross-section of

0.2 \times 10^{- 4} m^{2}

and the other is of steel with

0.1 \times 10^{4} m^{2}

cross-section. In order to have equal stresses in the two wires, a weight should be hung from the rod from end

A

a distance of

A 2m long light metal rod AB is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One wire is of brass and has cross section of $0.2 \times 10^{- 4} m^{2}$ and the other is of steel with $0.1 \times 10^{- 4} m^{2}$ cross section. In order to have equal stress in the two wires, a weight is hang from the rod. The position of the weight along the rod from end A should be.

Q. A light rod of length

2.00 m

is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel of cross-section

10^{- 3} m^{2}

and the other is of brass of cross-section

2 \times 10^{- 3} m^{2}

. Find out the position along the rod at which a weight may be hung to produce equal stress in both the wires.

Given:

Y_{steel} = 2 \times 10^{11} {N/m}^{2}

Y_{brass} = 10^{11} {N/m}^{2}

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The correct options are A Both (a) and (b) are correct B The ratio of tension in the steel and brass wires is 0.5 C The load is suspended at a distance of 400/3cm from the steel wireT10.1=T20.2 or T1T2=12=0.5Further, T1x=T2(2−x)or T1T2=2−xxHence, 2−xx=0.5=12 or 4−2x=xor, x=43m=4003cm.