Question

plzzz solved the question 18th and 19th

Answer 1

18) frequency of sound by the whistle=v=400Hz

sound speed=340m/s

speed of wind,v=10m/s

as the qbserver is not moving, the frequency of sound heard by the observer is equal to the sound produced=400Hz

as the wind blows towards the observer, the effective speed of sound increases by 10 units=340+10=350m/s

the wave length of the sound heard by observer=350/400
                                                                             =0.875m


19) moment of inertia is a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.


I’ll perform the calculation in polar coordinates. Refer to the sketch above .Let the mass of the ring and its radius be MM and aa respectively. The mass of an infinitesimal segment adθadθ located at (a,θ)(a,θ) is dM=λadθdM=λadθ, where λ=M2πaλ=M2πa. The moment of inertia of this elementary mass about the tangent is dM(a−acosθ)2dM(a−acos⁡θ)2, the distance of the mass dMdM from the tangent being (a−acosθ)(a−acos⁡θ). Then, the moment of inertia of the circular ring about the tangent is ∫dM(a−acosθ)2=∫2πθ=0λadθ(a−acosθ)2=∫2πθ=0M2πaa(a−acosθ)2dθ=32Ma2