Escape Speed

Q. A satellite is launched into a circular orbit of radius ‘R’ around earth while a second satellite is launched into an orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is

1. 3
2. 0.7
3. 1
4. 1.5

Q. The potential energy of a body of mass $3\text{kg}$ on the surface of a planet is $54\text{J}$ Its escape velocity will be –

1. $162\text{m/s}$
2. $36\text{m/s}$
3. $18\text{m/s}$
4. $6\text{m/s}$

Q.

If $v_e$ and $v_o$ represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R, then

1. 

2. 

3. 

4. 

Q.

Escape velocity of a body on a planet is $100m{s}^{-1}$. What is the gravitational potential energy of the body at the surface, if the mass of the body is $1kg$?

1. - 5000 J

2. 5000 J

3. - 1000 J

4. - 2400 J

Q.

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

1. One

2. Two

3. Half

4. Infinity

Q.

A projectile rises upto a maximum distance of $\frac{R}{1-k^2}$ where K is a constant and R is the radius of Earth. If the velocity of the projectile with which it should be fired upwards from the surface of Earth to reach this height is equal to the product of a coefficient and escape velocity, then this coefficient is equal to:

1. K

2. K²

3. 

4. 

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.

Determine the escape velocity of a rocket on the far side of a moon of a planet. The radius of the moon is $2.64\times {10}^6$m and its mass is $1.495\times {10}^{23}$. The mass of the planet is $1.9\times {10}^{27}$kg, and the distance between planet and the moon is $1.071\times {10}^9$m. Include the gravitational effect of planet and neglect the motion of the planet and the moon as they rotate about their CM.

1. 1.560 X 10⁴ms^-1

2. 

3. 

4. 

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.

For a body to escape from earth, angle from horizontal at which it should be fired is

1. 0⁰

2. 45⁰

3. 90⁰

4. Any angle