$A$ particle of mass $m$ having negative charge $q$ moves along an ellipse around a fixed positive charge $Q$ such that its maximum and minimum distances from the fixed charge are $r_1$ and $r_2$ respectively. The angular momentum $L$ of this particle is:

$A$ very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R$ $(R << L)$. $A$ star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$,then:

Which of the following astronomers first proposed that the Sun is static and the Earth revolves around the Sun?

Answer the following:
$(a)$ You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
$(b)$ An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size,can he hope to detect gravity?
$(c)$ If you compare the gravitational force on the earth due to the sun to that due to the moon,you would find that the Sun's pull is greater than the moon's pull. However,the tidal effect of the moon's pull is greater than the tidal effect of the sun. Why?

$A$ particle of mass $m$ starts from rest at a distance $R$ from the centre and along the axis of a fixed ring of radius $R$ and mass $M$. Its velocity at the centre of the ring is:

The relative uncertainty in the period of a satellite orbiting around the Earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible,the relative uncertainty in the mass of the Earth is: