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Horizontal projectile and freely falling body

A rifle at a height H aimed horizontally fires a bullet to the ground. At the same time , a bullet with the same mass in dropped from the same height. Neglecting air resistance, which one hits the ground first?Explain.

ED posted

Answer:

Both will hit the ground simultaneously.

When a body is projected horizontally, its initial vertical velocity is zero and vertical acceleration is g, the acceleration due to gravity.

The values of a velocity and acceleration of a freely falling body are also the same.

So, both will hit the ground simultaneously

Is the acceleration due to gravity different in south pole and north pole

Mohak Tandon Asks – “

“Is the acceleration due to gravity different in south pole and north pole?”

Answer:

As per theory, acceleration due to gravity changes with altitude, depth and latitude.

If we consider that the variation of g with latitude is caused by rotation of earth only, then the value of g will be same for both north pole and south pole.

But, the change in the value of acceleration due to gravity with latitude is caused by the shape of earth too. So it depends your distance from the centre of earth when you are at north pole or south pole.

For calculations the polar radius is taken same at North as well as south pole. So, value of g can be taken the same for both poles.

Gravitation – Questionbank with answer for CBSE Class 9 SA1

The following questions are for a quick revision of the chapter “Gravitation” for CBSE Class 9. There are many other questions which can be asked from the portion allotted for SA1, but will mainly based on these concepts. The questions are based on the bare essential concepts; the minimum level of learning expected from the children

  1. State the universal law of gravitation.
    Universal law of gravitation states that every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
  2. Define G. Write its value with proper units of SI
    G is the universal constant of gravitation. It is defined as the gravitational force of attraction between two objects of mass 1 kg each separated by a distance of 1m. Its value is 6.67 x 10-11 Nm2kg-2
  3. What is the difference between gravity and gravitation?
    The force of gravitation exerted by earth (or any other planet) on the objects on its surface is called gravity. Every object attracts every other object due to the force of gravitation. So, Gravity is a special case of Gravitation
  4. Define acceleration due to gravity.
  5. Why the moon is not “falling” to earth?
  6. Derive an expression for the acceleration due to gravity.
  7. Write the differences between g and G.
  8. calculate the value of g on the surface of earth.
  9. Discuss the variation of g with height, depth and latitude.
  10. Distinguish mass and weight.

Variation of acceleration due to gravity with depth. A doubt.

Rajkumar asks: “accelaration due to gravity decrease on depth of earth with the relation of g’=g(1-2h/R). but with relation of g=GM/(R*R)  g increase.

Answer:

When the object is on the surface or above it, the entire mass of the earth attracts it. But when it is inside, the net attraction towards CENTRE is provided only by the mass of earth below it.

ie; if it is at a depth d below the surface, then it is attracted to the centre by a sphere of radius R-d only. The forces due to the rest of the mass of earth cancel out. (On one side there is a little mass and on the other side greater amount of mass but distributed faraway and both contribute equally towards force and cancel out.)

Time Period of a Simple Pendulum in Space

Mary Beth asked:

“if you set up a pendulum aboard an orbiting space vehicle, would the period be less than, the same as, or greater than it would be in our lab? explain.”

Ans:

In a space vehicle orbiting around the earth, the apparent weight is zero as the entire gravitational pull is being utilized in providing the centripetal force required for revolving. This is called weightlessness in space.

i.e; in effect, the acceleration due to gravity is zero which make the time period of the satellite infinity. The pendulum will not oscillate at all.

__________________________________________________________

Tailpiece:

However, in manned space vehicles, there is an option to simulate gravity by making the system rotate at a particular rate so as to make the inhabitants feel as if there is weight and gravity.

Pendulum on Mount Everest !

Michelle Guzman Asked:

If you set a pendulum atop Mt. Everest, would the period be less than, greater than or equal to the period you would get in the lab?  Explain.

Ans:

As you know, the acceleration due to gravity decreases as we go upwards from surface of earth.

The time period of a simple pendulum is given by

Where l is the length of the pendulum, and g is the acceleration due to gravity.

From the equation, we can conclude that, the Time period of the pendulum increases (i.e. it goes slower)  if the pendulum is set up on top of Mount Everest.

For Creative and Critical Thinkers

Here we have not considered the change in temperature between the laboratory conditions and the temperature on top of Mount Everest which is very low. A decrease in temperature would decrease the length of the pendulum (Unless it is made up of such a substance which does not change its length with change in  temperature) and will also decrease the time period of the pendulum, making it move faster.

My first answer is correct only if the laboratory conditions are the same as on top of Mt. Everest or vice versa, except for the difference in altitude (height)

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