An air bubble produced due to a mild explosion inside sea- water is executing a harmonic motion. The time period of this motion, `T prop p^(a) d^(b) E^( c)` , where p = pressure d = density and E = energy released in the explosion. Determine the values of a,b and c from dimensional analysis.

If a,b,c,d,e are in A.P., then the value of (a+b+5c-5d+e) in terms of a is-

If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

It two physical quantities a and b are related by the equation a= kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a prop b if a and b are of the same dimension. If a particle of mass m executes simple harmonic motion with amplitude A and frequency f, then its energy is proportional to

It two physical quantities a and b are related by the equation a = kb where k is dimensionless constant, then the principle of dimensional homogeneity demands that a and b have the same dimension. However the proportionality constant k cannot be determined by dimensional analysis only. It may at most be written that a prop b if a and b are of the same dimension. Time period (T) of oscillation of a liquid drop depends on its radius r the density rho and the surface tension sigma of the liquid. Then T is proportional to

Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|, where a ,b ,a n d c are respectively, the pth, qth, and rth terms of a harmonic progression.

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to 1 b. 2 c. 2^n d. 2^(2n)

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq= 1 decay. s^(-1) . After how many days the activity of Iodine-131 will be 1/16 th of its initial value. [The half-life of Iodine-131 is 8 d.] (A) 24 d (B) 32 d (C) 40 d (D) 48 d

Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) If the peak value of electric field at a point in electromagnetic wave is 15 V . m^(-1) , then average electrical energy density (in j . m^(-3) )