Consider a binary star system of star A and star B with masses m_A and m_B revolving in a circular orbit of radii r_A an r_B, respectively. If T_A and T_B are the time period of star A and star B, respectively,

Then :

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s² and 4 m/s² respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take g = 10 ms^$$-$$2, the radius of earth, R = 6400 $$\times$$ 10³ m, Take $$\pi$$ = 3.14]

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $${\overrightarrow L }$$. The magnitude of the areal velocity of the planet is :