Home
Class 11
PHYSICS
When composite rod is free, composite le...

When composite rod is free, composite length increase to `2.002m` from temperature `20^(@)C` to `120^(@)C`. When composite rod is fixed between the support, there is no change in component length. Find `Y` and `alpha` of steel if
`Y_(cu) = 1.5 xx 10^(13) N//m^(2)` and `alpha_(cu) = 1.6 xx 10^(-5//@)C`

Text Solution

Verified by Experts

`Deltal = l_(s)alpha_(s)DeltaT + l_(c)alpha_(c)DeltaT`
`.002 = [1.5 alpha_(s) + 0.5 xx 1.6 xx 10^(-5)] xx 100`
`alpha_(s) = (1.2 xx 10(-5))/(1.5) = 8 xx 10^(-6)//^(@)C`
there is no change in component in length
For steel
`x = l_(s) alpha_(s) DeltaT - (Fl_(s))/(AY_(s)) = 0`

`(F)/(AY_(s)) = alpha_(s)Delta_(s) ....(A)`
for copper
`x = (Fl_(c))/(AY_(c)) - l_(c)alpha_(c)DeltaT = 0`
`(F)/(AY_(c)) = alpha_(c)DeltaT ...(B)`
`B//A rArr (Y_(s))/(Y_(c)) = (alpha_(c))/(alpha_(s))`
`Y_(s) = Y_(c) (alpha_(c))/(alpha_(s)) = (1.5 xx 10^(13) xx 16 xx 10^(6))/(8 xx 10^(-6)) = 3 xx 10^(13N//m^(2)`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY AND VISCOCITY

    RESONANCE|Exercise Exercise- 1 PART - I|8 Videos

  • ELASTICITY AND VISCOCITY

    RESONANCE|Exercise Exercise- 1 PART - II|14 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 92 illustration|2 Videos

  • ELECTROMAGNETIC INDUCTION

    RESONANCE|Exercise Exercise|43 Videos

Similar Questions

Explore conceptually related problems

When composite rod is free, composite rod is free, compositive length increase to 2.002m from temprature 20^(@)C to 120^(@)C . When composite rod is fixed between the support. There is no change in component length. Find Y and alpha of steel if Y_(cu) = 1.5 xx 10^(13 N//m^(2) alpha_(cu) = 1.6 xx 10^(-5//@)C

When composite rod is free, then composite length increases to 2.002 m for temperature 20^(@)C to 120^(@)C when composite rod is fixed between the support there is no change in component length find y and alpha of steel, if y_(c)=1.5xx10^(13)N//m^(2)alpha_(c)=1.6xx10^(-5)//.^(@)C .

What should be the length of steel and copper rods at 0^(@)C that the length of steel rod is 5 cm longer than copper at all termperature? Given alpha_(Cu) = 1.7 xx 10^(5) .^(@)C^(-1) and alpha_(steel) = 1.1 xx 10^(5) .^(@)C^(-1) .

The length of the steel rod which would have the same difference in length with a copper rod of length 24cm at all temperatures. (alpha_("copper") = 18 xx 10^(-6) K^(-1) alpha_("steel") = 12 xx 10^(-6) k^(-1)) is -

A brass of length 2 m and cross-sectional area 2.0 cm^(2) is attached end to end to a steel rod of length and cross-sectional area 1.0 cm^(2) . The compound rod is subjected to equal and oppsite pulls of magnitude 5 xx 10^(4) N at its ends. If the elongations of the two rods are equal, the length of the steel rod (L) is { Y_(Brass) = 1.0 xx 10^(11) N//m^(2) and Y_(steel) = 2.0 xx 10^(11) N//m^(2)

A rod has been laid by using alternate rails of steel and aluminium each 12m long in a winter season when temperature is .-2^(@)C . The maximum temprature which can must be left be-tween advance rules of they are just to touch on a summer day (alpha_("steel") = 1.2 xx 10^(-5) ^(0)C^(-1) alpha_(Al) = 2.4 xx 10^(-5) ^(0)C^(-1)

A rod of length 2 m is at a temperature of 20^@ C. find the free expansion of the rod, if the temperature is increased to 50^@ C, then find stress produced when the rod is (i) fully prevented to expand, (ii) permitted to expand by 0.4mm. Y=2xx10^(11)N//m^(2), alpha=15xx10^(-6//^(@))C .

A rod of steel is 5m long and 3cm diameter at a tempearatyre if 20^(@)C . Find the free expansion of the rod when the temperature us raused ti 65^(@)C . Find the respective pulls exerted if (i) the ends do not yield and (ii) the ends yield by 0.12 cm. Y = 2 xx 10^(5) MN // m^(2) and alpha = 12 xx 10^(6) per ^(@)C

The length of a rod is exactly 1 m when measured at rest . What will be its length when it moves at a speed of (a) 3 xx 10^(5)m s ^(-1) (b) 3 xx 10^(6) m s^(-1) and ( c) 3 xx 10^(7) m s ^(-1) ?