Question

29
The answer to Q.5.226 of I.E. Irodov is A2 = -2,
cos O. Here symbols have their usual notations.
can represent
(A) kinetic energy
(C) force
(D) pressure
(B) power​

Answer 1

Explanation:

A. kinetic energy....

Answer 2

Answer:

The quantity, $\Psi$, in the equation represents the kinetic energy.

Explanation:

Assuming the given equation is

$\Delta\lambda=-\lambda\sqrt{\frac{2\Psi }{mv^{2} } } cos\theta$

Writing the dimensions for each physical quantity involved in the equation,

Wavelength, $[\lambda]=[L^{1} ]$

Mass, $[m]=[M^{1} ]$  

$velocity, [v]=[L^{1} T^{-1} ]$  

$[cos\theta]=\frac{adj}{hyp}= \frac{[L]}{[L]}$  

Substituting all in the equation, the dimensional formula can be written as

$[L^{1} ]=-[L^{1}]\sqrt{\frac{2\Psi }{[M^{1} ][L^{1} T^{-1} ]^{2}} }$

$\implies1=-\sqrt{\frac{2\Psi }{[M^{1} ][L^{1} T^{-1} ]^{2} }$

squaring on both sides

$\implies1=\frac{2\Psi }{[M^{1} ][L^{1} T^{-1} ]^{2} }$

$\implies [{\Psi }]= {[M^{1} ][L^{1} T^{-1} ]^{2} }$

$\implies [{\Psi }]={[M^{1} L^{2} T^{-2} ] }$

${[M^{1} L^{2} T^{-2} ] }$ is the dimensional formula for kinetic energy.

Therefore, the quantity, $\Psi$, in the equation represents the kinetic energy.

So, the correct answer is option (A).