Escape Speed

Q.

A machine gun fires 60 bullets per minute with a velocity of 700m/s . If the mass of each bullet is 50g , calculate the power of gun .

Q.

Derive an expression for lateral shift and normal shift. On what factors these depends

Q.

A particle on earth's surface is given a velocity equal to its escape velocity. Its total mechanical energy will be

1. Infinite

2. Positive

3. Negative

4. Zero

Q. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass $=5.98\times {10}^{24}\text{kg}$) have to be compressed to be a black hole?

1. ${10}^{-9}\text{m}$
2. ${10}^{-6}\text{m}$
3. $100\text{m}$
4. ${10}^{-2}\text{m}$

Q. The escape velocity for a planet is $v_e$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the center of the planet, its speed will be

1. $v_e$
2. $\frac{v_e}{2}$
3. $\frac{v_e}{\sqrt{2}}$
4. Zero

Q.

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

1. R/3

2. R/2

3. R/4

4. R/5

Q.

The escape velocity from the earth is about $11km{s}^{-1}$. The escape velocity from a planet having twice the radius and the same mean density as the earth, is

1. 22 km / s

2. 11 km / s

3. 5.5 km / s

4. 15.5 km / s

Q. The time period of a satellite moving in a circular orbit around a planet is independent of

1. the mass of the satellite.
2. the mass of the planet.
3. all the three parameters.
4. the radius of the planet.

Q. Width of a slab is 6cm whose μ= 3/2. If rear surface is silvered and object is placed at a dis†an ce 28 cm from front face. Calculate the final position of the image from the silvered surfac

Q. A particle is projected vertically upwards from the surface of the earth (radius $R)$ with a speed equal to one-fourth of escape velocity. The maximum height attained by it from the surface of the earth is

1. $\frac{R}{5}$
2. $\frac{R}{10}$
3. $\frac{R}{15}$
4. $\frac{R}{20}$

Q.

If the earth stops rotating about its axis, then the magnitude of gravity

1. Will not change at the poles

2. All of the above

3. Increases everywhere on the surface of earth

4. Will increase only at the poles

Q. Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

1. 
2. 
3. 
4. 

Q. A ball, whose kinetic energy is E, is projected at an angle of ${45}^{\circ }$ from the horizontal. What will be it's kinetic energy at the highest point of its flight?

Q.

A space-ship is put into a circular orbit close to Earth's surface. What additional velocity must be imparted to the ship so that it is able to escape the gravitational pull of Earth(approximately)? $(R=6400km,g=9.8\frac{m}{s^2})$

1. 11.2 km/s

2. 3.3 km/s

3. 6.8 km/s

4. 9.3 km/s

Q. The kinetic energy needed to project a body of mass $m$ from the earths surface (radius $R$) to infinity is

1. $\frac{1}{4}$ $mgR$
2. $\frac{1}{2}$ $mgR$
3. $mgR$
4. $\frac{1}{3}$ $mgR$

Q.

For satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

1. $\frac{1}{\sqrt{2}}$

2. $2$

3. $\frac{1}{2}$

4. $\sqrt{2}$

Q.

Define angle of projection.

Q. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11{\text{kms}}^{–1}$, the escape velocity from the surface of the planet would be

1. $1.1{\text{kms}}^{–1}$
2. $11{\text{kms}}^{–1}$
3. $110{\text{kms}}^{–1}$
4. $0.11{\text{kms}}^{–1}$

Q.

A beam of diameter d is incident on a glass hemisphere as shown in figure. If the radius of curvature of the hemisphere is very large in comparison to d, then diameter of the beam at the base of the hemisphere will be

1. d

2. $\frac{3d}{4}$

3. $\frac{d}{3}$

4. $\frac{2d}{3}$

Q. If $V_e$ is the escape velocity and $V_0$ is the orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

1. $V_0=\sqrt{2}{V}_e$
2. $V_0=V_e$
3. $V_e=\sqrt{2V_0}$
4. $V_e=\sqrt{2}{V}_0$

Q.

The energy required to accelerate a car from 10m/s to 20m/s is x times the energy required to accelerate the same car from 0 to 10m/s.calculate the value of x?

Q.

The radius of the earth is $6400km$ and $g=10m{s}^{-2}$. In order that a body of $5kg$ weights zero at the equator, the angular speed of the earth is (in rad/sec)

1. $\frac{1}{80}$

2. $\frac{1}{400}$

3. $\frac{1}{800}$

4. $\frac{1}{600}$

Q. Pertaining to two planets, the ratio of escape velocities from respective surfaces is $1:2$ , the ratio of the time period of the same simple pendulum at their respective surfaces is $2:1$ (in same order). Then the ratio of their average densities is

1. $1:1$
2. $1:2$
3. $1:4$
4. $8:1$

Q. A projectile of mass $m$ is fired from the surface of the earth at an angle $\theta ={60}^{\circ }$ with the vertical. The initial speed $v_o$ is equal to $\sqrt{\frac{G{M}_e}{R_e}}$. How high does the projectile rise$?$ Neglect air resistance and the earth's rotation.

1. $\frac{Re}{2}$
2. $\frac{Re}{5}$
3. $\frac{Re}{4}$
4. $\frac{Re}{8}$

Q.

In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be

1. 

2. 

3. 

4. 

Q. Two planets have same density but different radii.The accelaration due to gravity would be

1. same on both planets
2. greater on the planet with smaller radius
3. greater on the planet with larger radius
4. depending on the distance of planet from the Sun

Q.

If the density of a small planet is the same as that of the earth while the radius of the planet is $0.2$ times that of the earth, the gravitational acceleration on the surface of the planet is _____.

1. $0.2g$

2. $0.4g$

3. $2g$

4. $4g$

Q. Charges of $-2\times {10}^{-10}C,2\times {10}^{-10}$ and $4\times {10}^{-10}C$ are placed at the corners A, B and D of a square ABCD of side 2m. Calculate the resultatnt field at the centre of the square.

1. $0.9\sqrt{2}N{C}^{-1}$
2. $1.8N{C}^{-1}$
3. $0.9N{C}^{-1}$
4. $3.6N{C}^{-1}$

Q. The minimum and maximum distances of a satellite revolving around earth are $2R$ and $6R$ respectively. Where $R$ is radius of earth. The maximum velocity of satellite is :-

1. $\sqrt{\frac{GM}{R}}$
2. $\sqrt{\frac{3GM}{2R}}$
3. $\frac{1}{2}\sqrt{\frac{3GM}{R}}$
4. $\sqrt{\frac{3GM}{R}}$

Q. Escape velocity from earth is about $11km{s}^{-1}$. Escape velocity from a planet having twice the radius and same mean density as the earth is.

1. $22km{s}^{-1}$
2. $15.5km{s}^{-1}$
3. $5.5km{s}^{-1}$
4. $11km{s}^{-1}$