A satellite is orbiting the earth. If its distance from the earth is increased, its

1

(a)

angular velocity would increase

(b)

linear velocity would increase

(c)

angular velocity would decrease

(d)

time period would increase

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth,is

1

(a)

\(\frac{1}{2}mgR\)

(b)

2mgR

(c)

mgR

(d)

\(\frac{1}{4}mgR\)

If three uniform spheres, each having mass M and radius r, are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

1

(a)

\(\frac{GM^2}{4r^2}\)

(b)

\(\frac{2GM^2}{r^2}\)

(c)

\(\frac{2GM^2}{4r^2}\)

(d)

\(\frac{\sqrt 3GM^2}{4r^2}\)

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1

(a)

gx

(b)

\(\frac{gR}{R-x}\)

(c)

\(\frac{gR^2}{R+x}\)

(d)

\((\frac{gR^2}{R+x})^{\frac{1}{2}}\)

Mars has about 1/10th as much mass as the earth and half as great a diameter. TI1e acceleration of a falling body on Mars is about

1

(a)

9.8 m s^-2

(b)

1.96 ms^-2

(c)

3.92 m s^-2

(d)

4.9 m s^-2

How earth retains most of the atmosphere?

1

(a)

Earth retains most of the atmosphere due to force of gravity.

If earth be at one half its present distance from the sun, then how many days will there be in a year?

1

(a)

\(T^{ 2 }\alpha R^{ 3 }\)
\(\\ Hence,\quad \quad \frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } =\frac { { R }_{ 1 }^{ 3 } }{ { R }_{ 2 }^{ 3 } } \Rightarrow { T }_{ 2 }^{ 2 }=\left[ \frac { { R }_{ 2 } }{ { R }_{ 1 } } \right] ^{ 3 }T_{ 1 }^{ 2 }\)
\(\\ \Rightarrow T_{ 2 }=T_{ 1 }\left[ \frac { R_{ 2 } }{ { R }_{ 1 } } \right] ^{ 3/2 }=365\left( \frac { R/2 }{ R } \right) ^{ 3/2 }\)
\(\\ =365\times \frac { 1 }{ \sqrt [ 2 ]{ 2 } } =129\ days\)

By which law is the Kepler's law of areas identical?

1

(a)

The law of conservation of angular momentum.

Do the force of friction and other contact forces arise due to gravitational attraction? If not, then what is the origin of these forces?

1

(a)

Contact forces have electrical region.

Is the Kepler's law kinematic?

1

(a)

Yes, because kepler's third law is the relation between distance and time.