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Two point masses 2M amd M are kept on a smooth
horizontal surface at a separation of r. Due to
gravitational pull they move towards each
other.They will meet at point:
1. r/2 from initial position of M
2. 2r/3 from initial position of M
3. r/3 from initial position of M
4. they will not meet

Two point masses each of value m are at separation
r. Due to mutual gravitational force they revolve in
a circle with constant separation. What is the
speed of each point mass ?
1. $\sqrt{\frac{\mathrm{Gm}}{\mathrm{r}}}$
2. $\sqrt{\frac{\mathrm{Gm}}{{\mathrm{r}}^2}}$
3. $\sqrt{\frac{\mathrm{Gm}}{2\mathrm{r}}}$
4. $\frac{{\mathrm{Gm}}^2}{2\mathrm{r}}$

When a body of mass m is sent to a height of R/4
from the earth's surface, R being radius of earth, g
is the acceleration due to gravity on the surface of
earth, the potential energy increases by
1. $\frac{\mathrm{mgR}}{3}$
2. $\frac{\mathrm{mgR}}{4}$
3. $\frac{\mathrm{mgR}}{5}$
4. $\frac{\mathrm{mgR}}{6}$

The escape velocity from the surface of a planet is
V. The escape velocity from a planet having twice
the radius and the same mean density as the former
is:
1. 2V                2. V
3. V/2               4. None of these

At what depth inside the earth the value of
acceleration due to gravity becomes one- fourth of
that on earth's surface ? Radius of earth is R:
1. 3R/4              2. R/2
3. R/4                4. R

If gravitational force of attraction between a planet
and a star around which planet revolve, is
proporational to R^-5/2 then the square of period of
revolution (T2) is proporational to, R being radius
of orbit:
1. R³                      2. R^3/2
3. R^7/2                   4. R³

A planet moves around the sun. At a point P it is
closest to the sun at a distance d1 and has a speed
v1. At another point Q when it is farthest from the
sun at a distance d2, its speed will be:
1.  d₁v₁/d₂ 
2. d₂v₁/d₁
3. ${\mathrm{d}}_1^2{\mathrm{v}}_1/{\mathrm{d}}_2$
4. ${\mathrm{d}}_2^2{\mathrm{v}}_1/{\mathrm{d}}_1^2$
 

A satellite is moving in a circular orbit around earth.
If gravitational pull suddenly disappear, then it:
1.  Continues to move with the same speed along
the same path
2. Moves with same speed tangential to the
original orbit
3. Falls down with increasing speed
4. Becomes static after moving a certain distance
along the original path

The ratio of accleration due to gravity at the
surfaces of the two planets having same density
but radii R₁ and R₂, is:
1. R₁/R₂ 
2. R₂/R₁
3. (R₁/R₂)² 
4. (R₂/R₁)²

A satellite moves around the earth in a circular
orbit of radius with speed V. If the mass of the
satellite is M, its total energy is:
1. $-\frac{1}{2}{\mathrm{MV}}^2$
2. $\frac{1}{2}{\mathrm{MV}}^2$
3. $\frac{3}{2}{\mathrm{MV}}^2$
4. ${\mathrm{MV}}^2$

The difference in acceleration due to gravity at heights
h₁ and h₂ from earth's surface, h₂ - h₁ = h and h₂, h₁<<
R, the radius of earth is, the mean density of earth is
$\mathrm{\rho }$ ,
1. $\frac{8}{3}\mathrm{\pi Mh}$
2. $\frac{8}{3}\mathrm{\pi \rho h}$
3. $\frac{8}{3}\mathrm{G\pi \rho h}$
4. $\frac{2\mathrm{GMh}}{{\mathrm{R}}^3}$

The height of the point vertically above the earth's
surface, at which acceleration due to gravity
becomes 1% of its value at the surface is (Radius
of earth = R):
1. 8 R             2. 9 R
3. 10 R           4. 20 R

Gravitational potential at distance R/2 from centre
of a hollow thin shell of mass M and radius R is:
1. $-\frac{2\mathrm{GM}}{\mathrm{R}}$
2. $-\frac{\mathrm{GM}}{2\mathrm{R}}$
3. $\frac{\mathrm{GM}}{\mathrm{R}}$
4. $-\frac{\mathrm{GM}}{\mathrm{R}}$

An artificial satellite moving in a circular orbit
around the earth has a kinetic energy E₀. Its potential
energy is:
1. - E₀ 
2. E₀
3. 2 E₀ 
4. - 2 E₀

The mean radius of the earth is R, its angular speed
about its own axis $\mathrm{\omega }$ and the acceleration due to
gravity at earth surface is g. The cube of radius of
orbit of a geostationary satellite be:
1. $\frac{{\mathrm{R}}^2\mathrm{g}}{\mathrm{\omega }}$
2. $\frac{{\mathrm{R}}^2\mathrm{\omega }}{g}$
3. $\frac{\mathrm{Rg}}{{\mathrm{\omega }}^2}$
4. $\frac{{\mathrm{R}}^2\mathrm{g}}{{\mathrm{\omega }}^2}$

What would be the minimum velocity of projection
of body from the surface of earth so that it may rise
a height equal in radius of earth from the surface ?
Radius of earth = R, mass of earth = M
1. $\sqrt{\frac{\mathrm{GM}}{2\mathrm{R}}}$
2. $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$
3. $\sqrt{\frac{\mathrm{GM}}{3\mathrm{R}}}$
4. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}$

The figure shows the motion of a planet around
the sun S in an elliptical orbit with the sun at the
focus. The shaded areas A and B can be assumed
to be equal. If t₁ and t₂ represent the time taken for
the planet to move from a to b and c to d
respectively, then:

1. ${\mathrm{t}}_1<{\mathrm{t}}_2$
2. ${\mathrm{t}}_1>{\mathrm{t}}_2$
3. ${\mathrm{t}}_1={\mathrm{t}}_2$
4. None

Earth is rotating about its axis with uniform speed $\mathrm{\omega }$. When it suddenly stops, the value of acceleration due to gravity at latitude 45$°$ is increased by (Radius of earth is R):
1. ${\mathrm{\omega }}^2\mathrm{R}$
2. $\frac{{\mathrm{\omega }}^2\mathrm{R}}{2}$
3. $\frac{{\mathrm{\omega }}^2\mathrm{R}}{\sqrt{2}}$
4. ${\mathrm{\omega }}^2\mathrm{R}\sqrt{2}$

Two bodies of masses m₁ and m₂ are initially at
rest at infinite distance apart. They are then allowed
to move towards each other under mutual
gravitational attraction. Their relative velocity of
approach at a separation distance r between them
is:
1. ${\left[\frac{2\mathrm{G}\left({\mathrm{m}}_1-{\mathrm{m}}_2\right)}{\mathrm{r}}\right]}^{1/2}$
2. ${\left[\frac{2\mathrm{G}\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}{\mathrm{r}}\right]}^{1/2}$
3. ${\left[\frac{r}{2G{m}_1{m}_2}\right]}^{1/2}$
4. ${\left[\frac{2\mathrm{G}}{\mathrm{r}}{m}_1{m}_2\right]}^{1/2}$

Suppose the gravitational force varies inversely as
the n^th power of distance. Then the time period of a
planet in a circular orbit of radius R around the sun
will be proportional to:
1. ${\mathrm{R}}^{\mathrm{n}}$
2. ${\mathrm{R}}^{\frac{\mathrm{n}-2}{2}}$
3. ${\mathrm{R}}^{\frac{\mathrm{n}-1}{2}}$
4. ${\mathrm{R}}^{\frac{\mathrm{n}+1}{2}}$