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Consider a ‘beam expander’ which consists of two converging lenses of focal lengths 40 cm and 100 cm having a common optical axis. A laser beam of diameter 2 mm is incident on the 40 cm focal length lens. Then what is the diameter (in mm) of the final beam (see figure)?

Solution: diameter of beam, 2x=2mm Focal length of lenses, f1=40cm and f2=100cm \(\begin{array}{l}\frac{x}{f_{1}}=\frac{y}{f_{2}}\end{array} \) \(\begin{array}{l}\frac{1}{40}=\frac{y}{100}\end{array} \) y= 5 mm 2y... View Article

Two artificial satellites of masses m1 and m2 are moving with speeds v1 and v2 in orbits of radii r1 and r2 respectively. If r1 >r2, then which of the following statements is true?

a) \(\begin{array}{l}v_{1}=v_{2}\end{array} \) b) \(\begin{array}{l}v_{1}> v_{2}\end{array} \) c) \(\begin{array}{l}v_{1}<v_{2}\end{array} \) d) \(\begin{array}{l}\frac{v_{1}}{r_{1}}\frac{v_{2}}{r_{2}}\end{array} \) Solution: c) \(\begin{array}{l}v_{1}<v_{2}\end{array} \) Orbital velocity, \(\begin{array}{l}v... View Article

A rigid vessel of volume 0.50m^3 containing H2 at 20.5 degree C and a pressure of 611×10^3 Pa connected to a second rigid vessel of volume 0.75m^3 containing Ar at 31.2 degree C at a pressure of 433×10^3 Pa. A valve separating the two vessels is opened and both are cooled to a temperature of 14.5 degree C. What is the final pressure in the vessels?

Solution: \(\begin{array}{l}n_{T}=n_{1}+n_{2}\end{array} \) \(\begin{array}{l}\frac{PV}{RT}=\frac{P_{1}V_{1}}{RT_{1}}+\frac{P_{2}V_{2}}{RT_{2}}\end{array} \) \(\begin{array}{l}\frac{P(1.25)}{14.5+273}=\frac{611*10^{3}*0.5}{20.5+273}+\frac{433*10^{3}*0.75}{31.2+273}\end{array} \) \(\begin{array}{l}P=\frac{287.5}{1.25}(2106.73)\end{array} \) \(\begin{array}{l}P=4.84*10^{5} Pa\end{array} \)

Ekuverin Exercise

Ekuverin exercise is a joint military exercise held between the two neighbouring nations- India and Maldives. It has been in... View Article