Mass of our galaxy Milky Way, M = 2.5 × 1011
solar mass Solar mass = Mass of Sun = 2.0 × 1036 kg
Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036 = 5 ×1041 kg
Diameter of Milky Way, d = 105 ly
7 Radius of Milky Way, r = 5 × 104 ly
1 ly = 9.46 × 1015 m
∴ r = 5 × 104 × 9.46 × 1015
= 4.73 ×1020 m
Since a star revolves around the galactic centre of the Milky Way, its time period is given by the relation:
\(T = (\frac{4π^2 \,r^3 }{ GM})^{\frac{1}{2}}\)
\(= (\frac{4 × (3.14)^2 × (4.73)^3 × 10^{60} }{6.67 ×10 ^{-11 }× 5 × 10^{41}}) ^{\frac{1}{2}} =\frac{ 39.48 × 105.82 ×10^{30} }{33.35 }) ^{\frac{1}{2}}\)
\(=(125.27 × 10^{30} )^{\frac{1}{2}} = 1.12 × 10^{16}\) s
1 year = 365 x 324 x 60x60 s
\(1s = \frac{1}{365 ×324 × 60×60}\) year
\(∴ 1.12 × 10^{16}s = \frac{1.12 × 10^{16} }{365 × 324 × 60×60}\)
\(= 3.55× 10 ^8 \) years
A small point of mass \(m\) is placed at a distance \(2R\) from the center \(O\) of a big uniform solid sphere of mass \(M\) and radius \(R\). The gravitational force on \(m\) due to \(M\) is \(F_1\). A spherical part of radius \(R/3\) is removed from the big sphere as shown in the figure, and the gravitational force on \(m\) due to the remaining part of \(M\) is found to be \(F_2\). The value of the ratio \( F_1 : F_2 \) is:
The height from Earth's surface at which acceleration due to gravity becomes \(\frac{g}{4}\) is \(\_\_\)? (Where \(g\) is the acceleration due to gravity on the surface of the Earth and \(R\) is the radius of the Earth.)
Find the mean and variance for the following frequency distribution.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
Gravitational force is a central force that depends only on the position of the test mass from the source mass and always acts along the line joining the centers of the two masses.
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
By combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2 [f(r)is a variable, Non-contact, and conservative force]