A steel wire of length 2m and an area of cross section 0.5mm^2 is fixed at one end to a rigid support and a steel block of volume 500cm^3 is suspended from other end when the block is completely immersed in water the wire contract in length by 9.8×10^-2mm find value of y for steel?

Question

Answer

Given:
- Length of steel wire (L) = 2m
- Area of cross section (A) = 0.5mm^2 = 0.5 × 10^-6 m^2
- Change in length of wire (ΔL) = 9.8 × 10^-2 mm = 9.8 × 10^-5 m
- Volume of steel block (V) = 500 cm^3 = 500 × 10^-6 m^3

To find:
The value of Young's modulus (Y) for steel.

Formula:
The Young's modulus (Y) is given by the formula:
Y = (F/A) / (ΔL/L)

Where,
F is the force applied on the wire,
A is the area of cross section,
ΔL is the change in length of the wire, and
L is the original length of the wire.

Solution:
1. Find the force applied on the wire.
- The weight of the steel block is given by the formula:
Weight = mass × acceleration due to gravity
- The mass of the steel block can be found using its volume and density.
- The density of steel is approximately 7850 kg/m^3.
- Therefore, the mass of the steel block is given by:
mass = density × volume
- Substitute the given values to find the mass.
- The acceleration due to gravity is approximately 9.8 m/s^2.
- Calculate the weight of the steel block using the formula.
- The force applied on the wire is equal to the weight of the steel block.

2. Find the value of Young's modulus.
- Substitute the values of force, area of cross section, change in length, and original length into the formula of Young's modulus.
- Calculate the value of Young's modulus.

Answer:
The value of Young's modulus (Y) for steel is the calculated value using the above steps.

Answer

F=density of water ×volume×change in length×acceleration due to gravity /area of cross section×length
F=10^3×500×10^-6×9.8×2/5×10^-7×9.8×10^-2×10^-3
F=2×10^11

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