Home
Class 11
PHYSICS
A light rod of length of length 2 m is ...

A light rod of length of length `2 m` is suspended from a 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 `10^(-3) m^(2)` and the other is of brass of cross- section `2xx10^(-3) m^(2).x` is the distance from the steel wire end, at which a weight may be hung. ` Y_(steel) = 2xx10^(11) Pa and Y_(brass) = 10^(11) Pa`
Which of the following statement(s) is /are correct ?

A

`x= 1.2 m` , if the strains of both the wires are to be equal

B

` x= 1.42 m` , if the stresses of the wires are to be equal

C

`x= 1m` , if the stains of both the wires are to be equal

D

` x = 1.33 m`, if the stresses of the wires are to be equal

Text Solution

Verified by Experts

If stress in steel = stress in brass,
then `(T_(s))/(A_(S)) = (T_(B))/(A_(B))`
`(T_(S))/(T_(B)) = (A_(S))/(A_(B)) = (10^(-3))/(2xx10^(-3)) = 1/2` ...(i)
System is in equilibrium n. So, taking moments about `P`
` T_(S)'x = T_(B)(2-x) rArr (T_(S))/(T_(B)) = (2-x)/x` ...(ii)
If strain in steel = strain in brass ,
then ` (T_(S)//A_(S))/Y_(S) = (T_(B)//A_(B))/Y_(B) = ((10^(-3)) ( 2xx10^(11)))/((2xx10^(-3))(10^(11))) = 1` ...(iii)
From Eqs. (ii) and (iii) , we get `x= 1 m `
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY

    DC PANDEY|Exercise Level 2 Comprehension Based|6 Videos

  • ELASTICITY

    DC PANDEY|Exercise Level 2 Subjective|10 Videos

  • ELASTICITY

    DC PANDEY|Exercise Level 2 Single Correct|10 Videos

  • CURRENT ELECTRICITY

    DC PANDEY|Exercise All Questions|434 Videos

  • ELECTROSTATICS

    DC PANDEY|Exercise Integer|17 Videos

Similar Questions

Explore conceptually related problems

A light rod of length 4.0 m is suspended from the ceiling horizontally by means of two vertical wire of equal length tied to its ends. One of the wires is made of steel and is of cross-section 10^(-3)m^(2) and the other is of brass of cross-section 2xx10^(-3)m^(2) . Find out the position along the rod at which a weight may be hung to produce equal stresses in both wires.

A light rod of length 2 m is suspended ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is ade of steel and is of cross-section 0.1 cm and the other of brass of cross-section 0.2 cm. Along the rod at what distance a weight may be hung to produce stresses in the wires? (Y_("Steel") = 2 xx 10^(11) Nm^(-2), Y_("Bass") = 1 xx 10^(11) Nm^(-2))

A light rod AC 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 and is of cross-section 10^(-3) m^(2) and the other is of brass of cross-section 2xx10^(-3) m^(2) . The position of point D from end A along the rod at which a weight may be hung to produce equal stress in both the wires is [Young's modulus of steel is 2xx10^(11) Nm^(2) and for brass is 1xx10^(11) Nm^(-2) ]

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 cm^(2) . The other wire is a brass of cross section 0.2 cm^(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?

Alight rod of length 2 m is suspended horizontlly from the ceiling bty means of two vertical wirs of equal length tied to its ends One wire is mode of steel and is of cross - section 0.1 sq cm and the other is of brass of cross -section 0.2 sq cm Find the postion along the rod at which a wight may be hung to produce (i) equal stress in both wirs (ii) equal strain in both wires (Y for brass =10xx10^(10) Nm^(-2) and Y "for steel" =20xx10^(10) Nm^(-2) )

A light rod of length L=2 m is suspended horizontally from the ceiling by two wires A and B of equal lengths. The wire A is made of steel with the area of cross section A_(S)=1xx10^(-5)m^(2), while the wire B is made of brass of cross sectional area A_(b)=2xx10^(-5)m^(2). A weight W is suspended at a distance x from the wire A as shown in figure. Take, Young's modulus of steel and brass as Y_(s)=2xx10^(11)Nm^(-2) and Y_(b)=1xx10^(11)Nm^(-2) . Determine the value of x so that equal strains are produced in each wire

A light rod of length L=2 m is suspended horizontally from the ceiling by two wires A and B of equal lengths. The wire A is made of steel with the area of cross section A_(S)=1xx10^(-5)m^(2), while the wire B is made of brass of cross sectional area A_(b)=2xx10^(-5)m^(2). A weight W is suspended at a distance x from the wire A as shown in figure. Take, Young's modulus of steel and brass as Y_(s)=2xx10^(11)Nm^(-2) and Y_(b)=1xx10^(11)Nm^(-2) . Determine the value of x so that equal stresses are produced in each wire.