Home
Class 11
PHYSICS
A rubber cord 10 m long is suspended ver...

A rubber cord `10 m` long is suspended vertically. How much does it stretch under its own weight (Density of rubber is `1500 kg//m, Y=5xx10 N//m,g = 10 m//s`)

A

`15xx10` m

B

`7.5 xx 10` m

C

`12 xx 10` m

D

`25 xx 10` m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of how much a rubber cord stretches under its own weight, we will use the formula for elongation due to the weight of the cord. ### Step-by-Step Solution: 1. **Identify the Given Values:** - Length of the rubber cord, \( L = 10 \, \text{m} \) - Density of rubber, \( \rho = 1500 \, \text{kg/m}^3 \) - Young's modulus, \( Y = 5 \times 10^8 \, \text{N/m}^2 \) - Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) 2. **Calculate the Weight of the Cord:** The weight of the rubber cord can be calculated using the formula: \[ \text{Weight} = \text{Volume} \times \text{Density} \times g \] The volume of the cord is given by: \[ \text{Volume} = \text{Cross-sectional area} \times \text{Length} \] However, for this problem, we can directly use the formula for elongation under its own weight. 3. **Use the Formula for Stretching:** The elongation (\( \Delta L \)) of the cord due to its own weight can be calculated using the formula: \[ \Delta L = \frac{L^2 \rho g}{2Y} \] where: - \( L \) is the length of the cord, - \( \rho \) is the density, - \( g \) is the acceleration due to gravity, - \( Y \) is Young's modulus. 4. **Substituting the Values:** Now substitute the known values into the formula: \[ \Delta L = \frac{(10 \, \text{m})^2 \times (1500 \, \text{kg/m}^3) \times (10 \, \text{m/s}^2)}{2 \times (5 \times 10^8 \, \text{N/m}^2)} \] 5. **Calculating the Numerator:** \[ \Delta L = \frac{100 \times 1500 \times 10}{2 \times 5 \times 10^8} \] \[ = \frac{1500000}{10 \times 10^8} \] \[ = \frac{1500000}{10^9} \] \[ = 1.5 \times 10^{-3} \, \text{m} \] 6. **Final Result:** Thus, the stretch of the rubber cord under its own weight is: \[ \Delta L = 1.5 \times 10^{-3} \, \text{m} = 0.0015 \, \text{m} = 1.5 \, \text{mm} \] ### Conclusion: The rubber cord stretches by **1.5 mm** under its own weight.
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY

    ERRORLESS |Exercise Bulk Modulus|21 Videos

  • ELASTICITY

    ERRORLESS |Exercise Rigidity Modulus|18 Videos

  • FLUID MECHANICS

    ERRORLESS |Exercise Fluid Mechanics|19 Videos

Similar Questions

Explore conceptually related problems

An Indian rubber cord 10 cm long is suspended vertically. How much does it stretch under its own weight ? (rho=1500 kg//m^(3), Y=5xx10^(8)N//m^(2), g=10m//s^(2))

The breaking stress for a substance is 10^(6)N//m^(2) . What length of the wire of this substance should be suspended verticaly so that the wire breaks under its own weight? (Given: density of material of the wire =4xx10^(3)kg//m^(3) and g=10 ms^(-12))

A rubber string 10m long is suspended from a rigid support at its one end. Calculate the extension in the string due to its own weight. The density of rubber is 1.5xx10^(3) and Young's modulus for the rubber is 5xx10^(6)Nm^(-2) Take g=10Nkg^(-1) .

A rubber cord of density d, Young's modulus Y and length L is suspended vertically . If the cord extends by a length 0.5 L under its own weight , then L is

Find the terminal velocity of solid shpere or radius 0.1 m moving in air in vertically downward direction . (eta=18xx10^(-5) Ns//m^(2) , density of sphere =1000 kg//m^(2) and g=10^m//s^(2))

An Indian rubber cord L metre long and area of cross-section A "metre"^(2) is suspended vertically. Density of rubber is D "kg/metre"^(2) . If the wire extends by l metre under its own weight, then extension l is

A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given: Young's modulus of elasticity of rubber = 5 xx 10^(6) N//m and density of rubber =1.5xx10^(3)kg//m^(3) . Take g=10ms^(-12))

Find the terminal velocity of solid sphere of radius 0.1 m moving in air in vertically downward direction. (eta=1.8xx10^(-5)(Ns)/(m^(2)) , density of sphere =1000(kg)/(m^(3)) and g=10(m)/(s^(2)))

For steel, the breaking stress is 8 xx 10^(6) N//m^(2) . What is the maximum length of a steel wire, which can be suspended without breaking under its own weight? [ g = 10 m//s^(2) , density of steel = 8 xx 10^(3) kg//m^(3) ]

Density of rubber is d. A thick rubber cord of length L and cross-section area. A undergoes elongation under its own weight on suspending it. This elongation is proportional to