Home
Class 12
PHYSICS
A rod of length l and coefficient of lin...

A rod of length l and coefficient of linear expansion `alpha`. Find increase in length when temperature changes from T to T+ `DeltaT`

A

`l alpha DeltaT`

B

`l (1+alpha DeltaT)`

C

`l (1+ 2alpha DeltaT)`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the increase in length of a rod when the temperature changes, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Problem**: We have a rod of initial length \( L \) and a coefficient of linear expansion \( \alpha \). We want to find the increase in length when the temperature changes from \( T \) to \( T + \Delta T \). 2. **Identify the Formula for Linear Expansion**: The formula for the change in length \( \Delta L \) due to thermal expansion is given by: \[ \Delta L = L \cdot \alpha \cdot \Delta T \] where: - \( \Delta L \) is the change in length, - \( L \) is the original length of the rod, - \( \alpha \) is the coefficient of linear expansion, - \( \Delta T \) is the change in temperature. 3. **Calculate the Change in Temperature**: The change in temperature \( \Delta T \) can be calculated as: \[ \Delta T = (T + \Delta T) - T = \Delta T \] 4. **Substitute Values into the Formula**: Now, substitute the values into the linear expansion formula: \[ \Delta L = L \cdot \alpha \cdot \Delta T \] 5. **Final Result**: The increase in length of the rod when the temperature changes from \( T \) to \( T + \Delta T \) is: \[ \Delta L = L \alpha \Delta T \] ### Conclusion: The increase in length of the rod is given by: \[ \Delta L = L \alpha \Delta T \]
Promotional Banner

Similar Questions

Explore conceptually related problems

The temperature of an isotropic cubical solid of length l_(0) , density rho_(0) and coefficient of linear expansion alpha is increased by 20^(@)C . Then at higher temperature , to a good approximation:-

A thin rod, length L_(0) at 0^(@)C and coefficient of linear expansion alpha has its two ends mintained at temperatures theta_(1) and theta_(2) respectively Find its new length .

If two rods of length L and 2L having coefficients of linear expansion alpha and 2alpha respectively are connected so that total length becomes 3L, the average coefficient of linear expansion of the composite rod equals

Two metallic rods of length l and 3l have coefficient of linear expansion alpha and 3alpha respectively. The coefficient of linear expansion ofr their series combinations, is

An isosceles triangles is formed with a thin rod of length l_(1) and coefficient of linear expansion alpha_(1) , as the base and two thin rods each of length l_(2) and coefficient of linear expansion alpha_(2) as the two sides. The distance between the apex and the midpoint of the base remain unchanged as the temperature is varied. the ratio of lengths (l_(1))/(l_(2)) is

Two metal rods of lengths L_(1) and L_(2) and coefficients of linear expansion alpha_(1) and alpha_(2) respectively are welded together to make a composite rod of length (L_(1)+L_(2)) at 0^(@)C. Find the effective coefficient of linear expansion of the composite rod.

There are two rods of length l_1 l_2 and coefficient of linear expansions are alpha_1 and alpha_2 respectively. Find equivalent coefficient of thermal expansion for their combination in series.

find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion alpha ) about its perpendiuclar bisector when itsw temperature is slightly increased by Delta T.

Two rods each of length L_(2) and coefficient of linear expansion alpha_(2) each are connected freely to a third rod of length L_(1) and coefficient of expansion alpha_(1) to form an isoscles triangle. The arrangement is supported on a knife-edge at the midpoint of L_(1) which is horizontal. what relation must exist between L_(1) and L_(2) so that the apex of the isoscles triangle is to remain at a constant height from the knife edge as the temperature changes ?