Tag: escape velocity

Questions Related to escape velocity

Time period of simple pendulum in a satellite is

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. Infinite

  2. Zero

  3. 2 sec

  4. Cannot be calculated

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Correct Option: A
Explanation:

Time period of simple pendulum is given by:
$\displaystyle T = 2\pi \sqrt{\frac{l}{g}}$
where l is the length of the pendulum.
Inside a satellite, $g = 0$
Hence, period will be infinite which means there will be no oscillation.

The percentage increase in earth's angular velocity so that all bodies lying on the equator feel weightlessness is nearly:

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. 17%

  2. $\dfrac{100}{17}$%

  3. 1600%

  4. 1700%

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Correct Option: A

For satellite in elliptical orbit which of the following quantities does not constant 

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. Angular momentum

  2. Momentum

  3. Areal velocity

  4. Total Energy

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Correct Option: B

If an astronaut comes out of the artificial satellite, then

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. He flies off tangentially

  2. He falls to the earth

  3. He performs SHM

  4. He continues to move along the satellite of the same orbit

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Correct Option: A

A person sitting in a chair in a satellite feels weightless because

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. the earth does not attract the object in a satellite.

  2. the normal force by the chair on the parson balance the earht's attraction.

  3. the normal force is zero.

  4. the person is satellite is not accelerated.

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Correct Option: C
Explanation:

As a person sits in a chair $($ on Earth's surface $)$, he will experience two forces, the force of the Earth's gravitational field pulling him downward toward the Earth and the force of the chair pushing him upward. The upward chair force is sometimes referred to as a normal force.
If there were no upward normal force acting upon body, body would not have any sensation of the weight. Without the contact force $($ the normal force $)$, there is no means of feeling the non-contact force $($ the force of gravity $)$.
Hence, A person sitting in a chair in a satellite feels weightless because normal force is zero.

To overcome the effect weightlessness in an artificial satellite

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. the satellite is rotated around its axis with compartment of astronaut at the centre of the satellite.

  2. the satellite is shaped like wheel.

  3. the satellite is rotated around and around till weightlessness disappears.

  4. the compartment of astronaut is kept on the periphery of rotating wheel like satellite.

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Correct Option: D
Explanation:

On a rotating body, as we move away from center of rotation the centrifugal force increases. So, the centrifugal force is maximum at the periphery of a rotating wheel. Thus, having the astronaut room there would solve some of the weightlessness problem in satellite.

The time period of a second's pendulum inside a satellite will be

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. zero

  2. $1$ sec

  3. $2$ sec

  4. infinite

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Correct Option: D
Explanation:

time period $\propto \sqrt { \cfrac { l }{ g }  } $ , as in the satellite there will be no gravity so the time period will be infinite.(logical explanation. : without gravity there will be no force on pendulum so it will not move a bit even in infinite time.)

In an earth satellite moving in a circular orbit, a piece of metal weighing $16g$ (on the earth) is weighed by a spring balance while the metal is suspended in water. If the relative density of the metal is $8$, what weight will be recorded?

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. $-2$ g

  2. zero

  3. $2$ g

  4. $14$ g

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Correct Option: B
Explanation:

In the satellite the spring is in free fall so no weight will be recorded.

The radius and mean density of the earth are $R$ & $p$ respectively . the critical orbital speed of a satellite for a low altitude orbit is 

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. $ 2 \sqrt {\dfrac { \pi G p}{3R}} $

  2. $ 2R \sqrt {\dfrac { \pi Gp}{3}} $

  3. $ 2R \sqrt {\dfrac {2 \pi G p}{3}} $

  4. $ 2R \sqrt {\dfrac { \pi Gp}{2}} $

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Correct Option: B

An astronaut, inside an earth satellite, experiences weightlessness because

physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

  1. no external force is acting on him

  2. he is falling freely

  3. no reaction is exerted by the floor of the satellite

  4. he is far away from the earth's surface

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Correct Option: B,C
Explanation:

For an earth satellite moving in a circular orbit, centripetal force required for its circular motion is provided by the gravitational force exerted by earth on it.
 It means resultant force on the astronaut is equal to the gravitational force exerted by earth on him. Hence, no reaction is exerted by floor of the satellite on him.
In other words, his acceleration towards earth centre (centripetal acceleration) is exactly equal to acceleration caused by the gravitational force alone.
Hence, options (b) and (c) are correct.