According to Kepler's law of planetary motion if T represents time period and r is orbital radius, then for two planets these are related as

• ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^3 = {\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2$

• ${\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right)}^{3/2} = \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}$

• $\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right) = {\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^3$

• $\left(\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}\right) = {\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^{3/2}$

If the mass of moon is $\frac{1}{90}$ of earth's mass, its radius is $\frac{1}{3}$ of earth's radius and if g is acceleration due to gravity on earth, then the acceleration due to gravity on moon is

• $\frac{\mathrm{g}}{3}$

• $\frac{\mathrm{g}}{90}$

• $\frac{\mathrm{g}}{10}$

• $\frac{\mathrm{g}}{9}$

A rocket of initial mass 1000 kg ejects mass at a constant rate of 10 kg/s with constant relative speed of 11 ms^-1. Neglecting gravity, the acceleration of the rocket 1 min after the blast is

• 11/40 ms^-2

• 22/40 ms^-2

• 1.1/40 ms^-2

• 1 ms^-2

A research satellite of mass 200 kg circles the earth in an orbit of average radius 3R/2, where R is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earth's surface to be 10 N, the pull on the satellite will be

• 880 N

• 889 N

• 890 N

• 892 N

If the acceleration due to gravity is 10 ms^-2 and the units of length and time are changed to kilometre and hour respectively, the numerical value of the acceleration due to gravity is

• 360000

• 72000

• 36000

• 129600

Mass of the earth has been determined through

• use Kepler's T²/R³ constancy law

• sampling the density of earth's crust and using R

• Cavendish's determination of G and using R and g at surface

• use of periods of satellites at different heights above earth's surface

67.

The period of moon's rotation around the earth is nearly 29 days. If moon's mass were 2 fold its present value and all other things remained unchanged, the period of moon's rotation would be nearly

• $29\sqrt{2} \mathrm{days}$

• $\frac{29}{\sqrt{2}} \mathrm{days}$

• 29 × 2 days

• 29 days

Observers on 10th, 5th and ground floor of a tall building measure the velocity of certain rain drop by some accurate method. Surprisingly the velocity of rain drop measured by the three observers is found to be same. This is because

• there is no gravitational force acting on the drop

• gravitational force on the rain drop is balanced by force produced by surrounding air

• gravitational force on the rain drop is balanced by upward force of attraction produced by the cloud

• data is insufficient to predict

Weight of a body ofmass m decreases by 1 % when it is raised to height h above the earth's surface. If the body is taken to a depth h in a mine, change in its weight is

• 0.5 % decrease

• 2 % decrease

• 0.5 % decrease

• 1 % increase

If M is the mass ofthe earth and R its radius, the ratio of the gravitational acceleration and the gravitational constant is

• $\frac{{\mathrm{R}}^2}{\mathrm{M}}$

• $\frac{\mathrm{M}}{{\mathrm{R}}^2}$

• MR²

• $\frac{\mathrm{M}}{\mathrm{R}}$