Kepler's Law

Q. A quantity 𝑓 is given by $f=\sqrt{\frac{h{c}^5}{G}}$ where 𝑐 is speed of light, 𝐺 universal gravitational constant and ℎ is the Planck's constant. Dimension of 𝑓 is that of

1. momentum
2. area
3. volume
4. energy

Q. A hollow spherical shell is compressed to half of its radius, the gravitational potential at the centre.

1. increases
2. decreases
3. remains same
4. During the compression increases and then returns at the previous value.

Q.

A planet of mass $m$ moves around the sun of mass $M$ in an elliptical orbit. The maximum and minimum distances of the planet from the sun are $r_1$ and $r_2$ respectively. The time period of the planet is proportional to

1. $(r_1+r_2)$

2. ${(r_1+r_2)}^{1/2}$

3. ${(r_1–r_2)}^{3/2}$

4. ${(r_1+r_2)}^{3/2}$

Q. A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance ' $3a$ ' from the centre will be

1. $\frac{GM}{3a^2}$
2. $\frac{GM}{9a^2}$
3. $\frac{2GM}{3a^2}$
4. $\frac{2GM}{9a^2}$

Q.

By what percent the energy of a satellite has to be increased to shift it from an orbit of radius r to $\frac{3}{2}r$?

1. 66.7%

2. 33.3%

3. 15%

4. 20.3%

Q.

The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be

1. 83 minutes

2. 664 minutes

3. 249 minutes

4. 

Q.

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of earth

1. The total mechanical energy of S varies periodically with time

2. The linear momentum of S remains constant in magnitude

3. The acceleration of S is always directed towards the centre of the earth

4. The angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant

Q. The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of ${45}^{\circ }$ with the vertical, the escape velocity will be

1. $11\sqrt{2}km{s}^{-1}$
2. $22km{s}^{-1}$
3. $11km{s}^{-1}$
4. $\frac{11}{\sqrt{2}}km{s}^{-1}$

Q. A far off planet is estimated top be at a distance D from the earth . if its diametrically opposite extremes subtend an angle of ⚾ at an observatory situated on the earth , the apparx diameter of the planet is

Q.

Mass M is divided into two parts xM and (1 − x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum is

1. 

2. 

3. 

4. 

Q.

A saturn year is 29.5 times the earth's year. How far is the saturn from the sun if the earth is 1.50*10^8 km away from the sun?

Q. Which of the following curve represents the variation of gravitational potential of a hollow sphere of radius $R$ with radial distance $\left(r\right)$?

1. 
2. 
3. 
4. 

Q.

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $\left(\omega \right)$ and the distance of the planet from sun (r). If so the correct relation for areal velocity is

1. 

2. 

3. 

4. 

Q.

Do the centre of mass and centre of gravity coincide?

Q.

The surface of the earth receives solar radiation at the rate of 1400 $W{m}^{-2}$. The distance of the centre of the sun from the surface of the earth is $1.5\times {10}^{11}m$ and the radius of the sun is $7.0\times {10}^{8}m$. Treating the sun as a back body, it follows from the above data that the surface temperature of the sun is about

1. 5900 K

2. 6100 K

3. 5800 K

4. 6000 K

Q. If distance between the earth and the sun were half its present value, the number of days in a year would have been approximately

1. 64.5
2. 129
3. 182.5
4. 730

Q.

If a graph is plotted between $t^2$ and $r^3$ for a planet then its slope will be ____________

Q. A satellite of mass $m$ revolves around earth of mass $M$ in a circular orbit of radius $r$ with angular velocity $\omega$. If radius of the orbit becomes $9r$, then angular velocity of the satellite in the new orbit will be

1. $9\omega$
2. $\frac{\omega }{9}$
3. $27\omega$
4. $\frac{\omega }{27}$

Q. The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of ${45}^{\circ }$ with the vertical, the escape velocity will be

1. 
2. 
3. 
4. 

Q. What is geostationary satellite and what is the time period taken by it orbiting the earth?

Q. Two satellites $S_1$ and $S_2$ revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are $1\text{hour}$ and $8\text{hours}$ respectively. The radius of the orbit of $S_1$ is ${10}^4\text{km}$. When $S_1$ is closest to $S_2$, the angular speed of $S_2$ as observed by an astronaut in $S_1$ is :

1. $\pi \text{rad/hr}$
2. $\pi /3\text{rad/hr}$
3. $2\pi \text{rad/hr}$
4. $\pi /2\text{rad/hr}$

Q.

Orbit of a planet around a star is

1. A circle

2. An ellipse

3. A parabola

4. A straight line

Q. A satellite can be in a geostationary orbit around earth at a distance $r$ from the center. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth, if its distance from the center is

1. $\frac{r}{2}$
2. $\frac{r}{2\sqrt{2}}$
3. $\frac{r}{(4{)}^{1/3}}$
4. $\frac{r}{(2{)}^{1/3}}$

Q.

Time $\left(T\right)$, Velocity $\left(C\right)$, and angular momentum $\left(h\right)$ is chosen as fundamental quantities instead of mass, length, and time. In terms of these, the dimension of mass would be

1. $\left[M\right]=\left[T^{-1}{C}^{-2}h\right]$

2. $\left[M\right]=\left[T^{-1}{C}^{2}h\right]$

3. $\left[M\right]=\left[T^{-1}{C}^{-2}{h}^{-1}\right]$

4. $\left[M\right]=\left[T{C}^{-2}h\right]$

Q.

The distance of neptune and saturn from sun are nearly ${10}^{13}$ and ${10}^{12}$ meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

1. 100

2. 

3. 

4. 

Q.

If the mass of the earth decreases by 25% and its radius increases by 50% then the acceleration due to gravity at its surface decreases by nearly:

1. 89%

2. 67%

3. 33%

4. 11%

Q. The earth moves around the sun in an elliptical orbit as shown in figure. The ratio $\frac{OA}{OB}=x$. The ratio of the speed of the earth at B to that at A is nearly

1. 
2. 
3. 
4. 

Q.

Orbit of a planet around a star is

1. A circle

2. An ellipse

3. A parabola

4. A straight line

Q. A satellite revolves around the earth. Air pressure inside the satellite is maintained at 76 cm of Hg. What will be the height of mercury column in a barometer tube 1m long placed in the satellite.

Q.

Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?