The standard parameter of Earth is 398,600 km3/s2, distance between Earth and Mars is 225 x 106 km, force of gravitational attraction between Earth and Mars is 6.39 x 1023 N. What is the standard gravitational parameter of Mars? Given, universal gravitational constant is 6.67408 × 10-11 m3 kg-1 s-2.

S₁:A force of exists between everybody in the universe.
P :Normally it is very small but when the one of the bodies is a planet, like earth, the force is considerable.
Q :It has been investigated by many scientists including Galileo and Newton.
R :Everything on or near the surface of the earth is attracted by the mass of earth.
S :This gravitational force depends on the mass of the bodies involved.
S₆:The greater the mass, the greater is the earth's force of attraction on it. We can call this force of attraction gravity.

The Proper sequence should be:

A

PRQS

B

PRSQ

C

QSRP

D

QSPR

A sidereal day for Mars is 24.623 hours. ISRO is planning to put a satellite in geostationary orbit around Mars. What should be the altitude from the surface of Mars to achieve this goal? Radius of Mars is 3,389.5 km and gravitational parameter is 42,828 km3/s2.

A

17,038.14 km

B

25,012.11 km

C

20,427.64 km

D

13648.64 km

What is the force of attraction between earth and moon? Given, distance between earth and moon is equal to 384,400 km, standard gravitational parameter of earth is equal to 398,600 km3/s2 and mass of the moon is equal to 7.348 x 1022 kg.

A

1.982 x 1017 N

B

1.771 x 1026 N

C

2.042 x 1012 N

D

6.192 x 1017 N

What is the sidereal time period of a probe in a circular orbit around Mars? The probe is orbiting at an altitude of 500 km from the surface of Mars. Radius of Mars is 3,389.5 km and its mass is 6.39 x 1023 kg.

A

2.48 hrs

B

2.05 hrs

C

2.16 hrs

D

1.89 hrs

The radius of Mars is about half that of Earth; the mass of Mars is about one-tenth that of Earth. Which of the following is closest to the gravitational field at the surface of Mars?

A

10 N/kg

B

4 N/kg

C

2 N/kg

D

0.5 N/kg

Which of the following statements is/are false?
1. The value of G is the same as its value on the moon, on Earth.
2. The gravitational force between the centers of two masses of 2 kg placed at a distance of 1m is 26.68 × 10^-11 Nm²/kg².
3. The force is inversely proportional to the square of the distance between the two objects.
4. The force of gravity between two objects doubles when the distance between them is halved.

A

3 and 4 only

B

1 only

C

Only 4

D

2, 3 and 4

What is the velocity of a spacecraft in a circular orbit of 1,000 km from the surface of Mars? Radius of Mars is 3,389.5 km and its mass is 6.39 x 1023 kg.

A

7.233 km/s

B

4.525 km/s

C

3.117 km/s

D

3.989 km/s

A smooth plane inclined at an angle θ with the horizontal as shown in the given figure. A body starts from rest and slides down on the inclined surface. The time taken by the body to reach the bottom is

A

$$\frac{{\sqrt {2h} }}{g}$$

B

$$\sqrt {\frac{{2l}}{g}} $$

C

$$\frac{1}{{\sin \theta }}\sqrt {\frac{{2h}}{g}} $$

D

$$\sin \theta \frac{{\sqrt {2h} }}{g}$$

What is the specific energy of a spacecraft in an elliptical orbit around earth? Given, apogee and perigee distance from the surface of earth are 6250 km and 525 km respectively. The radius and standard gravitational parameter of earth are 6378 km and 398,600 km3/s2.

A

-30.3 km3/s2

B

40.2 km3/s2

C

-10.9 km3/s2

D

12.9 J/kg

Close-up images of Mars by the Mariner 9 probe indicated networks of valleys that looked like the stream beds on Earth. These images also implied that Mars once had an atmosphere that was thick enough to trap the sun's heat. If this were true, something happened to Mars billions of years ago that stripped away the planet's atmosphere.
This paragraph best supports the statement that

A

Mars now has little or no atmosphere.

B

Mars once had a thicker atmosphere than Earth does.

C

the <i>Mariner 9</i> probe took the first pictures of Mars.

D

Mars is closer to the sun than Earth is.

E

Mars is more mountainous than Earth is.