Tag: gravitation: planets and satellites

Questions Related to gravitation: planets and satellites

Weightlessness in a satellite is experienced because 

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

  1. of inertia

  2. the gravitational force acting on the satellite is zero

  3. of centre of gravity

  4. centrifugal acceleration negates the acceleration due to gravity

Show answer
Correct Option: D
Explanation:

The satellite rotates in a circular path or elliptical path such that gravitational pull is always balanced by centrifugal force due to the rotational motion of satellite.

Thus a body in the satellite will feel weightlessness.
although force of gravity on a body is never zero but it is balanced by centrifugal force in  this case.
so option D is correct.

A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to the rock.

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

  1. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite

  2. As the rock cannot generate its own force, it will slow down

  3. Gravity will pull the rock towards earth

  4. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity

  5. As the rock is smaller than the satellite, its inertia will pull it further away from earth

Show answer
Correct Option: A
Explanation:

The satellite moves in the orbit with a constant speed in circular path, with centripetal acceleration being provided by the force of gravity on it.

The radius of orbit can be found by 
$\dfrac{GMm}{R^2}=\dfrac{mv^2}{R}$
$\implies R=\dfrac{GM}{v^2}$ which is independent of the mass of projectile(satellite)
When the stone is released from the orbiting satellite, it moves with the same speed. Its mass is much lesser than that of satellite, but the orbital radius is independent of its mass, depending only upon the speed which is same. Thus is would also orbit the earth with same speed in same orbit as that of satellite.

A man weighs $75 kg$ on the surface of the earth. His weight in a geostationary satellite is:

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

  1. infinity

  2. $150 kg$

  3. zero

  4. $75/2 kg$

Show answer
Correct Option: C
Explanation:

A geostationary satellite revolves around the earths with the same time period of earth's rotation, that is 24 hours.
Since it revolves with same speed, the relative velocity is zero with respect to earth and hence any body inside a geostationary satellite doesn't feel the gravity.
So, the weight would be equal to zero.

A pendulum beats seconds on the earth. Its time period on a stationary satellite of the earth will be

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

  1. Zero

  2. $1\ s$

  3. $2\ s$

  4. Infinity

Show answer
Correct Option: D
Explanation:

Inside a satellite, every object experiences weightlessness

Therefore Time period of a pendulum inside a satellite is $T= 2\pi \sqrt{\cfrac{L}{g}}$
as $g=0$
$\therefore T=\infty$ (Infinity)
A pendulum beats seconds on the earth. Its time period on a stationary satellite of the earth will be Infinity.

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

Show answer
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%

Show answer
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

Show answer
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

Show answer
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.

Show answer
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.

Show answer
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.