1 The moon is observed from 2 diametrically opposite points A B on earth The angle teta - Physics - Physical World

Question

1 The moon is observed from 2
diametrically opposite points A & B on earth The angle teta
subtended at the moon by the 2 directions of observation is
1°54min Given that the diameter of earth is 1 276*10power 7
metre Calculate the distance of moon from earth
2 The Suns angular diameter is
1920sec The distance of Sun from earth is 1 496*10power11metre What
is the diameter of Sun
3 The escape velocity from surface
of earth is given by V=sq root of 2GM/R , where M is mass, R is
radius, G is universal gravitational constant Check the correctness
of this equation by using the method of dimension

Hansraj Rai · Accepted Answer

Dear Student!! Ans 1Using the parallax method, $θ = (1 + \frac{54}{60}) = {1 9}^{0} = 1 9 \times \frac{π}{180} = 0 033 r a d$ Distance of the moon from the earth, $= \frac{d}{θ} = \frac{1 276 \times 10^{7}}{0 033} = 38 67 \times 10^{7} m$ Ans 3 Writing the dimension on both the side of the equation $v = \sqrt{\frac{2 G M}{R}} [L T^{- 1}] = \sqrt{\frac{[M^{- 1} L^{3} T^{- 2}] [M]}{[L]}} [L T^{- 1}] = \sqrt{L^{2} T^{- 2}} L H S = R H S$ Dimension on the both side are equal, hence the formula is dimensionally correct