A mass of 100 gm is attached to the end of a rubber string 49 cm long n hving sn area of cross section 20 sqmm. The string is whirled around, horizontally at a cnstnt speed of 40 rps in a crcl of radius 51 cm. Find the young's modulus of rubber.

Doubt

To find the Young's modulus of rubber, we need to use the formula:

Young's modulus (Y) = (F/A) * (L/ΔL)

where:
F = Force applied on the rubber string
A = Cross-sectional area of the rubber string
L = Original length of the rubber string
ΔL = Change in length of the rubber string

Here's how we can find the Young's modulus step by step:

Step 1: Finding the force applied on the rubber string (F)
The force applied on the rubber string is the centripetal force required to keep the mass moving in a circular path. It can be calculated using the formula:

F = m * (v^2 / r)

where:
m = mass attached to the string
v = velocity of the mass in circular motion
r = radius of the circular path

Given:
Mass (m) = 100 gm = 0.1 kg
Velocity (v) = 40 rps * 2π * r (since v = ω * r, where ω is the angular speed in radians per second and r is the radius)
Radius (r) = 51 cm = 0.51 m

Calculating F:
F = 0.1 * (40 * 2π * 0.51)^2 / 0.51

Step 2: Finding the cross-sectional area of the rubber string (A)
Given:
Area of cross section (A) = 20 mm^2 = 20 * 10^-6 m^2

Step 3: Finding the original length of the rubber string (L)
Given:
Length (L) = 49 cm = 0.49 m

Step 4: Finding the change in length of the rubber string (ΔL)
The change in length of the rubber string is the increase in length caused by the force applied.

ΔL = L * F / (A * Y)

We can rearrange the formula to solve for Y:

Y = L * F / (A * ΔL)

Finally, we can substitute the values into the formula to get the Young's modulus of rubber.

find the force/area.

Force from centripetal force by
force=v^2/r (change rps to m/s)

then, you know the elongation, and the crosssectional area.

then solve for Young's modulus..
https://ccrma.stanford.edu/~jos/pasp/Young_s_Modulus_Spring_Constant.html