A body of mass 10 kg is attached to a wire 30 cm long. Area of cross section of the wire is 10 raise to power -6 metre square. It's breaking stress is 4.8×10 raise to power 7 N/metre square. Find maximum angular velocity with which it can be rotated in the horizontal circle?

force=w*length wire

breaking stress*Areawire=w*lengthwire
solve for w

To find the maximum angular velocity with which the body can be rotated in the horizontal circle, we need to consider the tension in the wire at the breaking point.

The tension in the wire can be calculated using the equation:

Tension = (Mass × Centripetal Force) / Radius

To find the centripetal force, we need to calculate the maximum force that can be exerted on the wire without exceeding its breaking stress. The maximum force can be found using the equation:

Maximum Force = Breaking Stress × Area of Cross Section

Now, we have all the required information to solve the problem:

Given:
Mass (m) = 10 kg
Length of wire (L) = 30 cm = 0.3 m
Area of Cross Section (A) = 10^-6 m^2
Breaking Stress (σ) = 4.8 × 10^7 N/m^2

Step 1: Calculate the maximum force:
Maximum Force = Breaking Stress × Area of Cross Section
Maximum Force = (4.8 × 10^7 N/m^2) × (10^-6 m^2)
Maximum Force = 48 N

Step 2: Calculate the tension in the wire:
Tension = (Mass × Centripetal Force) / Radius
Tension = (10 kg × Centripetal Force) / 0.3 m

Step 3: Set the tension equal to the maximum force and solve for the centripetal force:
Tension = Maximum Force
(Mass × Centripetal Force) / 0.3 m = 48 N
Centripetal Force = (48 N × 0.3 m) / 10 kg
Centripetal Force = 1.44 N

Step 4: Calculate the maximum angular velocity:
Centripetal Force = (Mass × Angular Velocity^2) × Radius
1.44 N = (10 kg × Angular Velocity^2) × 0.3 m
Angular Velocity^2 = 1.44 N / (10 kg × 0.3 m)
Angular Velocity^2 = 0.48 rad^2/s^2

Taking the square root of both sides,
Angular Velocity = √(0.48 rad^2/s^2)
Angular Velocity ≈ 0.69 rad/s

Therefore, the maximum angular velocity with which the body can be rotated in the horizontal circle is approximately 0.69 rad/s.