Shortcut Methods
Numerical Shortcuts :
 For Gravitational Force:
 Remember the formula  $$F = \frac{Gm_1m_2}{r^2}$$
 The value of G (gravitational constant) = 6.67×10^{11} N·m^{2}/kg^{2}
 For Orbital Velocity:
 $$v =\sqrt{GM/r}$$
 Remember that the orbital velocity is the velocity required by a satellite to remain in orbit around a planet or other celestial body.
 Use the value of G (6.67×10^{11} N·m^{2}/kg^{2}) and substitute the masses and distances appropriately.
 Motion under Gravity:
 Remember the equation:
 For Maximum height: $$v^2 = u^2 + 2as$$
 For Force acting $$F = mg$$

Buoyant Force:
 Use the formula: $$F_b = \rho ghV $$
 ρ is the density of the fluid,
 g is the acceleration due to gravity and
 V is the volume of the object submerged in the fluid.

For Density, remember the formula:
 ρ = m/V
 ρ is the density,
 m is the mass, and
 V is the volume.