Question 1 :
A tunnel is dug along a diameter of earth. The force on a particle of mass $m$ and distance $x$ from the centre in this tunnel will be :

Question 2 :
The orbital period of a satellite in a circular orbit of radius r about a spherical planet of mass M and density $\rho$ for a low altitude orbit r will be....

Question 3 :
A satellite in earth orbit experiences a small drag force as it enters the earth's atmosphere. Two students were asked consequence of this<br>Student-A : The satellite would slow down as, it spirals towards earth due to work of frictional force.<br>Student-B : The satellite speed up due to earths gravitational pull as it spirals towards earth.

Question 4 :
What should be the new radius of the earth in order to make the escape velocity to double of the present value without changing the mass of the earth, if the actual radius of the earth is equal to R?

Question 5 :
A particle falling under gravity describes $80 ft$ in a certain sec. How long does it take to describe next $112 ft$?$[g=32fts^{-2}]$

Question 6 :
<b></b>An object is weighed at the North pole by a beam&#160;balance and a spring balance, giving readings of&#160;$W_{B}$ and $W_{S}$ respectively. It is again weighed in&#160;the same manner at the equator, giving reading of&#160;$W'_{B}$ and $W'_{S}$ respectively. Assume that the&#160;acceleration due to gravity is the same everywhere and that the balances are quite sensitive.<br/>

Question 7 :
A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the<br/>acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is:&#160;

Question 8 :
The largest and the shortest distance of the earth from sun are a and b, respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on the major axis meets the orbit is