A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?

[Given ; Mass of planet = 8 × 10²² kg, Radius of planet = 2 × 10⁶ m, Gravitational constant G = 6.67 × 10^–11 Nm² /kg²]

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s)

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $${{7M} \over 8}$$ and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I₁ be the moment of inertia of the disc about its axis and I₂ be the moment of inertia of the new sphere about its axis. The ratio I₁/I₂ is given by :

In Li^{+ +}, electron in first Bohr orbit is excited to a level by a radiation of wavelength $$\lambda $$. When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $$\lambda $$?
(Given : H = 6.63 × 10^–34 Js; c = 3 × 10⁸ ms ^–1)