The depth x to which a bullet penetrates a human body depends on (i) coeffeicint of elasticity, `eta` and (ii) KE `(E_k)` of the bullet, By the method of dimensions, show that
`x prop ((E_k)/(eta))^(1//3)`

If the depth d to which a bullet of kinetic energy K can penetrate into a human body of modulus of electicity E, using the method of dimension, establish a relation between d, K and E . If K=cd^(x) E^(y) , fill x+y in OMR sheet. Modulus of elasticity =Force/Area , xx l/(Deltal)

The velocity of sound waves 'v' through a medium may be assumed to depend on : (i) the density of the medium 'd' and (ii) the modulus of elasticity 'E' . Deduce by the method of dimensions the formula for the velocity of sound . Take dimensional constant K=1.

Derive by the method of dimensions, an expression for the volume of a liquid flowing out per second through a narrow pipe. Asssume that the rate of flow of liwquid depends on (i) the coeffeicient of viscosity eta of the liquid (ii) the radius 'r' of the pipe and (iii) the pressure gradient (P)/(l) along the pipte. Take K=(pi)/(8) .

The time period 'T' of a body executing SHM may be supposed to depend upon (i) the amplitude 'A' , (ii) the force constant 'k' and (iii) the mass 'm' . Deduce by the method of dimensions the formula for T.

A lead bullet penetrates into a solid object and melts Assuming that 50% of its K.E. was used to heat it , calculate the initial speed of the bullet , The initial temp , of bullet is 27^(@)c and its melting point is 327^(@)C Latent heat of fasion of lead = 2.5 xx 10^(4) J kg^(-1) and sp heat capacity of lead = 1.25 J kg^(-1) K^(-1)

The electric field in a certain region is given by vec(E) = ((K)/(x^(3)))vec(i) . The dimensions of K are -

Explain how Einstein's photoelectric equation enables us to understand the (i) linear dependence, of the maximum K.E. of the emitted electrons, on the frequency of the incident radiations (ii) existance of a threshold frequency for a given photoemitter.

Name the process in which (i) momentum is conserved but K.E. is not conserved and (ii) momentum changes but K.E. dose not change.

The rotational K.E. of a body is given by (1)/(2) I omega^2. Use this equation to obtain the dimensions of I.