Escape Velocity

Q. The ratio of escape velocity of the earth to the escape velocity of the planet whose radius and mean density is twice as that of earth

Q. The ratio of the radius of the Earth to that of the moon is $10:1$. The ratio of g on earth to the moon is 6. The ratio of the escape velocity from the earth’s surface to that from the moon is approximately

1. 8
2. 2
3. 4
4. 10

Q. The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is

Q.

Calculate the escape velocity on the surface of the moon, if the mass and radius of the moon are $7.34\times {10}^{22}kg$ and $1.74\times {10}^{6}m$ respectively.

1. 2.37 m/s

2. 4.7 km/s

3. 2.37 km/s

4. 2 m/s

Q.

What do you mean by acceleration due to gravity?

Q. Calculate the escape velocity on the surface of the moon given the mass and radius of the moon to be $7.34\times {10}^{22}kg$ and $1.74\times {10}^{6}m$ respectively.

1. $5.62km/s$
2. $2.37km/s$
3. $1.27km/s$
4. $11.2km/s$

Q. A aeroplane moving horizontally With a speed 180 km/ hr drops a food packet while flying at a height of 490 m .the horizontal range is??

Q. An elephant and an ant are to be projected out of the earth into space. What is the velocity needed to do so?

1. Elephant needs to be projected with a higher velocity.
2. Both should be projected with the same velocity.
3. Ant should be projected with a higher velocity.
4. Elephant cannot be projected to space.

Q.

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the earth and one on the moon. Which of the following three statement(s) is/are true?
I. The horizontal distance traveled by the bullet is greater for the moon.
II. The time of flight is less for the bullet on the earth.
III. The velocity of the bullets at impact are the same.

1. III only

2. II only

3. I and II only

4. I and III only

Q. The escape velocity of a body in gravitational field of earth is independent of.

1. gravitational field of earth
2. its mass
3. radius of earth

Q.

What is approximate height of ozone layer in atmosphere? What role does it play for human survival?

Q.

The time period of an earth-satellite in circular orbit is independent of

1. The mass of satellite

2. Radius of the orbit

3. None of them

4. Both of them

Q.

Two satellites of masses 3m and m orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their orbital speeds is

1. $\sqrt{3}$

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

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

4. $1$

Q. A projectile is fired vertically upwards from the surface of the earth with a velocity $K{v}_e$, where $v_0$ is the escape velocity and $k<1$. If $R$ is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth, will be (neglect air resistance).

1. $R(1-k{)}^2$
2. $\frac{R}{1+k^2}$
3. $\frac{1-k^2}{R}$
4. $\frac{R}{1-k^2}$

Q. Acceleration due to gravity on a planet is $12$ times the value on the earth. Escape velocity for the planet and the earth are $V_p$ and $V_e$ respectively. The ratio of the radii of the planet and the earth is $1:2$, then

1. $V_p=\frac{V_e}{\sqrt{6}}$
2. $V_p=\sqrt{5}{V}_e$
3. $V_p=\sqrt{6}{V}_e$
4. $V_P=\frac{V_e}{6}$

Q.

A satellite is revolving around a planet in an orbit of radius$R$. Suddenly radius of orbit becomes $1.02R$, then what will be the percentage change in its time period of revolution?

1. $2\%$

2. $3\%$

3. $5\%$

4. $7\%$

Q. Escape velocity at earth's surface is $11.2km/s$. Escape velocity at the surface of a planet having mass $100$ times and radius $4$ times that of earth will be

1. $56km/s$
2. $112km/s$
3. $305km/s$
4. $11.2km/s$

Q.

A body is released from a point distance $r$ from the center of the earth. If $R$ is the radius of the earth and $r>R$, then the velocity of the body at the time of striking the earth will be

1. $\sqrt{gR}$

2. $\sqrt{2gR}$

3. $\sqrt{\frac{2gR}{r-1}}$

4. $\sqrt{\frac{2gR\left(r-R\right)}{r}}$

Q.

What Are Hyperbolas Used For?

Q.

A geo-stationary satellite is orbiting around earth at height of 30, 000 km in circular orbit. The radius of the earth is taken as 6000 km. The geo-stationary satellite comes back to its position after one revolution in exactly 24 hours. Let the acceleration due to gravity (g) be 10 $m/s^2$ and mass of satellite be 1000 kg; calculate the work done in 12 hours when moving under gravitational force.

1. $3.6\pi \times {10}^{14}J$

2. $2\pi \times 7.2\pi \times {10}^{14}J$

3. $1.8\pi \times {10}^{14}J$

4. $0J$

Q. What first is the first law of motion?

Q. Superman and Batman took part in a race. The race involved going from $A$ to $B$ {1 km straight line} and coming back to $A$ along the same line. Superman ran with a constant speed of $15$ m/s both ways. Batman on his way from $A$ to $B$ ran at a constant speed of $10$ m/s but on his way back cheated by using his car which moved at a speed of $20$ m/s. Who won the race?

1. Race ended in a tie
2. Data insufficient
3. Batman
4. Superman

Q. A body is projected up with a velocity equal to $3/4$ th of the escape velocity from the surface of the earth. The height reached by the body above the earth's surface is: (Radius of the earth is $R$)

1. $10R/9$
2. $9R/7$
3. $9R/8$
4. $10R/3$

Q. Derive the expression for escape velocity of a projectile from Earth.

Q. A particle is kept at rest at a distance $R$ (Earths radius) above the earths surface. The minimum speed with which it should be projected so that it does not return is

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

Q. The escape velocity from earth is 11 km/sec. The escape velocity from a planet having twice the radius and the same mean density as that of the earth is?

1. $11$
2. $22$
3. $33\sqrt{3}$
4. $44\sqrt{3}$

Q.

What is the ratio of the escape velocity of the Earth to orbital velocity on the Earth?

1. $\sqrt{2}$

2. 2

3. $\sqrt{3}$

4. 3

Q. How orbital and escape velocities are related?

1. $v_e=\sqrt{3}{v}_0$
2. $v_e=1.31v_0$
3. $v_e=2v_0$
4. $v_e=1.41v_0$

Q. At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere?(Given: Mass of oxygen molecule(m)$=2.76\times {10}^{-26}$kg
Boltzmann's constant $k_B=1.38\times {10}^{-23}J{K}^{-1}$)

1. $2.508\times {10}^4$K
2. $5.016\times {10}^4$K
3. $8.360\times {10}^4$K
4. $1.254\times {10}^4$K

Q. A simple pendulum in a lift moving up with a uniform acceleration ‘a’ has a time period $T_1$ and when the lift is moving down with the same acceleration has a time period $T_2$. If the lift were stationary, find the time period of that pendulum?

1. $T=\frac{\sqrt{2}{T}_2}{\sqrt{T_1^2+T_2^2}}$
2. $T=\frac{\sqrt{2}{T}_1{T}_2}{\sqrt{T_1^2+T_3^2}}$
3. $T=\frac{\sqrt{3}{T}_1{T}_2}{\sqrt{T_1^2+T_2^2}}$
4. $T=\frac{\sqrt{2}{T}_1{T}_2}{\sqrt{T_1^2+T_2^2}}$