A spherical asteroid having the same density as that of earth is floating in free space. A small pebble is revolving around the asteroid under the influence of gravity near the surface of the asteroid. What is the approximate time period of the pebble?

Aplanet of mass $m$ is in an elliptical orbit about the sun $(m < < M_{sun})$ with an orbital period $T.$ If $A$ be the area of orbit, then its angular momentum would be :

If the earth suddenly shrinks to $\frac{1}{64}$ th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{ x } h$. The value of $x$ is $.......$

If the radius of earth's orbit is made $1\frac{1}{4}$, the duration of an year will become

The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9 R$ is............ $T$

The mean radius of the earth's orbit round the sun is $1.5 \times {10^{11}}$. The mean radius of the orbit of mercury round the sun is $6 \times {10^{10}}\,m$. The mercury will rotate around the sun in