Show that if the rate of change of temperature with height `dT//dh` called lapse rate is a constant, a sound wave travelling horizontally is refracted along an arc of radius of curvature `rho=2T// (dT)/(dh)`

A ball was thrown at velocity of 10 m/s at 37^(@) to the horizontal. What is the rate of change of its speed when its radius of curvature is 51.2 m

A particle moves in the x-y plane according to the law x=t^(2) , y = 2t. Find: (a) velocity and acceleration of the particle as a function of time, (b) the speed and rate of change of speed of the particle as a function of time, (c) the distance travelled by the particle as a function of time. (d) the radius of curvature of the particle as a function of time.

The rate of reaction ((dx)/(dt)) varies with nature, physical state and concentration of reactants, temperature, exposure to light and catalyst, whereas rate constant (K) varies with temperature and catalyst only. The rate constant K is given as K=Ae^(-E_(a)//RT) where A is Arrhenius parameter or pre-exponential factor and E_(a) is energy of activation. The minimum energy required for a reaction is called threshold energy and the additional energy required by reactant molecules to attain threshold energy level is called energy of activation. For a chemical reaction: Ararr Product, the rate of disappearance of A is given by: (-dC_(A))/(dt)=K_(1) (C_(A))/(1+K_(2)C_(A)) . At low C_(A) , the order of reaction and rate constants are respectively:

The process by which a gas passes through a small hole into vacuum is called effusion. The rate of change of pressure(p) of a gas at constant temperature due to effusion of gas from a vessel of constant volume can be related to rate of change of number of molecules by the expression: (dp)/(dt)=(kT)/V((dN)/(dt)) where rate of change of number of molecules Rightarrow -((dN)/(dt))=(pA_(0))/(2pimkT)^(1//2) where k=Boltzmann constant N_(A) = Avogadro's number T= Temperature (in K) V= volume of vessel N=Number of molecules A_(0) = Area of aperture m=Mass of single molecule gamma=V/A_(0)sqrt((2pim)/(kT) If 2 g of SO_(2) effuses from given container in 10 sec then, mass of He effusing out in 30 seconds under identical conditions will be: