A body weight \(48~\text{N}\) on the surface of the earth. The gravitational force experienced by the body due to the Earth at a height equal to one-third the radius of the Earth from its surface is:
Question 2.
A body weighing \(100~\text{N}\) on the surface of the Earth weights \(x~\text{kg-ms}^{-2}\) at a height \(\frac{1}{9} R_E\) above the surface of Earth. The value of \(x\) is:
(take \(g= 10~\text{m}~ \text{s}^{-2}\) at the surface of Earth and \(R_E\) is the radius of Earth)
Question 3.
An object of mass \(100 ~\text{kg}\) falls from point \(A\) to \(B\) as shown in the figure. The change in its weight, corrected to the nearest integer (\(R_E\) is the radius of the Earth), is:
Question 4.
If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:
Question 5.
Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:
Question 6.
A body weighs \(72~\text{N}\) on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth?
Question 7.
A mass falls from a height \(h\) and its time of fall \(t\) is recorded in terms of time period \(T\) of a simple pendulum. On the surface of the earth, it is found that \(t=2T\). The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as \(t'\) and \(T'\). Then we can say:
Question 8.
A body weighs \(200\) N on the surface of the earth. How much will it weigh halfway down the centre of the earth?
Question 9.
If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?
Question 10.
The acceleration due to gravity at a height \(1~\text{km}\) above the earth's surface is the same as at a depth \(d\) below the surface of the earth. Then:
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Question 1.
Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:
Question 2.
The height at which the weight of a body becomes \(\left ( \frac{1}{16} \right )^\mathrm{th}\) of its weight on the surface of the earth (radius \(R\)) is:
Question 3.
A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:
Question 4.
Imagine a new planet having the same density as that of the Earth but \(3\) times bigger than the Earth in size. If the acceleration due to gravity on the surface of the earth is \(g\) and that on the surface of the new planet is \(g',\) then:
Question 5.
The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is \(R,\) the radius of the planet would be:
Question 6.
The acceleration due to gravity on planet \(A\) is \(9\) times the acceleration due to gravity on planet \(B\) . A man jumps to a height of \(2\) m on the surface of \(A\) . What is the height of a jump by the same person on planet \(B\) ?
Question 7.
When a body of weight 72 N moves from the surface of the Earth at a height half of the radius of the earth, then the gravitational force exerted on it will be:
Question 8.
For moon, its mass is \(\frac{1}{81}\) of Earth's mass and its diameter is \(\frac{1}{3.7}\) of Earth's diameter. If acceleration due to gravity at Earth's surface is \(9.8~\text{m/s}^2,\) then at the moon, its value is:
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