Explanation
The Sun’s diameter (d) = $${1.494\times {{10}^{11}}m}$$
And Sun’s angular diameter ($$\alpha $$) = $$1920''$$
To convert the angular diameter into radians, converting $$1920''$$into radians.
$$1''=4.85\times {{10}^{-6}}rad$$
⸫ $$1920''$$= $$1920\times 4.85\times {{10}^{-6}}=9.31\times {{10}^{-3}}rad$$= $$\alpha $$
Now, Sun’s diameter (D) = $$\alpha \times d$$
D = ($$9.31\times {{10}^{-3}}\times 1.494\times {{10}^{11}}$$)m
⸫ D = $$1.39\times {{10}^{9}}m$$
$$\textbf{Answer:}$$
$$\textbf{Hence, the correct option is (a)}$$ $$1.39\times {{10}^{9}}m$$
Hint: While rounding off measurements, we use the following rules by convention:
Step 1: finding the rounded off digits
Let us round off $$2.745$$ to $$3$$ significant figures.
Here the digit to be dropped is $$5$$, then the preceding digit is left unchanged because it is even.
Hence on rounding off $$2.745$$, it would be $$2.74$$.
Now consider $$2.737$$, here also the digit to be dropped is $$5$$, then the preceding digit is raised by one if it is odd.
Hence on rounding off $$2.735$$ to 3 significant figures, it would be $$2.74$$.
Correct option is (B) $$\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$$
Hint: Electric flux is the measure of the electric field lines crossing the surface.
Step1: Electric flux $$\phi=\int \vec{E} \cdot \vec{s}$$
The dimension of $$\phi=$$ dimension fo $$\mathrm{E} \times$$ dimension of $$\mathrm{s}$$
$$[\phi]=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right][\mathrm{AT}]^{-1}\left[\mathrm{~L}^{2}\right]=\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$$
Dimensional formula of:
$$E : [ML^{2}T^{-2}]\\$$
$$J : [ML^{2}T^{-1}]\\$$
$$G : [M^{-1}L^{3}T^{-2}]\\$$
Thus
$$(E J ^{2})/(M^{5} G^{2}) = \dfrac{[ML^{2}T^{-2}][ML^{2}T^{-1}]^{2}}{M^{5} \times [M^{-1}L^{3}T^{-2}]^{2}} \\$$
$$= \dfrac{[M^{3}L^{6}T^{-4}]}{[M^{3}L^{6}T^{-4}]}\\$$
$$= [M^{0} L^{0} T^{0}]$$
The above quantity is dimensionless. Angle is also a dimensionless quantity while others are having some dimensions.
Thus the correct option is D.
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