On doubling the distance between two masses, the gravitational force between them will:

Newton's law of gravitation is true for:

The gravitational force between two bodies is:

A body is in a state of rest at infinite distance. If it is made a satellite of Earth, which of the following physical quantities will be reduced?

The Earth is an approximate sphere. If the interior contained matter that is not of the same density everywhere, then on the surface of the Earth, the acceleration due to gravity:

Which of the following are true?

Q. 2 As observed from the earth, the sun appears to move in an approximately circular orbit. For the motion of another planet like mercury as observed from the earth, this would:

Q. 3 Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the centre of mass causing translation and net torque at the centre of mass causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere):

Q. 4 Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because:

Both the earth and the moon are subject to gravitational force of the sun. As observed from the sun, the orbit of the moon:

Q. 6 In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They:

Q. 7 Choose the wrong option.

Q. 8 Particles of masses 2M, m and M are respectively at points A, B and C with $AB=\frac{1}{2}\left(BC\right)$. The mass m is much-much smaller than M and at time t = 0, they are all at rest as given in the figure. At subsequent times before any collision takes place,

(a) m will remain at rest

(b) m will move towards M

(c) m will move towards 2M

(d) m will have oscillatory motion

Q. 9 Which of the following options are correct?

(a) Acceleration due to gravity decreases with increasing altitude.

(b) Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).

(c) Acceleration due to gravity increases with increasing latitude.

(d) Acceleration due to gravity is independent of the mass of the earth.

Q. 10 If the law of gravitation, instead of being inverse square law, becomes an inverse cube law:

(a) planets will not have elliptic orbits

(b) circular orbits of planets are not possible

(c) the projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic

(d) there will be no gravitational force inside a spherical shell of uniform density

Q. 11 If the mass of the sun were ten times smaller and gravitational constant G were ten times larger in magnitude. Then,

(a) walking on the ground would become more difficult

(b) the acceleration due to gravity on the earth will not change

(c) raindrops will fall much faster

(d) aeroplanes will have to travel much faster

If the sun and the planets carried huge amounts of opposite charges, then
a. all the three Kepler’s laws would still be valid
b. only the third law would be valid
c. the second law would not change
d. the first law would still be valid
Which of the above statements are correct?

Q. 13 There have been suggestions that the value of the gravitational constant G becomes smaller when considered over a very large time period (in billions of years) in the future. If that happens, for our earth,

(a) nothing will change

(b) we will become hotter after billions of years

(c) we will be going around but not strictly in closed orbits

(d) after a sufficiently long time, we will leave the solar system

Q. 14 Supposing Newton’s law of gravitation for gravitation forces $F_1$ and $F_2$ between two masses $m_1$ and $m_2$ at positions $r_1$ and $r_2$ read

$F_1=-F_2=-\frac{r_{12}}{r_{12}^3}G{M^2}_0{\left(\frac{m_1{m}_2}{M_0^2}\right)}^n$

where, $M_0$ is a constant of the dimension of mass, $r_{12}=r_1-r_2$ and n is a number. In such a case,

(a) the acceleration due to gravity on the earth will be different for different objects

(b) none of the three laws of Kepler will be valid

(c) only the third law will become invalid

(d) for n negative, an object lighter than water will sink in water

Q. 15 Which of the following are true?

(a) A polar satellite goes around the earth’s pole in the north-south direction.

(b) A geostationary satellite goes around the earth in the east-west direction.

(c) A geostationary satellite goes around the earth in the west-east direction.

(d) A polar satellite goes around the earth in the east-west direction.

Let the speed of the planet at the perihelion P in figure shown below be ${\mathrm{v}}_{\mathrm{P}}$ and the Sun-planet distance SP be ${\mathrm{r}}_{\mathrm{P}}$. Relation between $\left\{{\mathrm{r}}_{\mathrm{P}}, {\mathrm{v}}_{\mathrm{P}}\right\}$ to the corresponding quantities at the aphelion $\left\{{\mathrm{r}}_{\mathrm{A}}, {\mathrm{v}}_{\mathrm{A}}\right\}$ is:

Let the speed of the planet at the perihelion P in figure shown below be ${\mathrm{v}}_{\mathrm{P}}$ and the Sun-planet distance SP be ${\mathrm{r}}_{\mathrm{P}}$. Will the planet take equal times to traverse BAC and CPB ?

Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle? Take AG = BG = CG = 1 m.