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Practice each question, then open the answer or worked solution.
How is the gravitational force between two point masses affected when they are dipped in the water keeping the separation between them the same?
The gravitational force is unaffected by the medium, and it remains the same between the point masses irrespective of their surrounding. Therefore, when the two-point masses are dipped in water, the gravitational force between them remains the same.
Is it possible for a body to have inertia but no weight?
Yes, it is possible for a body to have inertia, but no weight, as inertia is associated with the mass of the body. A satellite revolving around the earth is an example of a body with inertia and has no weight.
We can shield a charge from electric fields by putting it side a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
No, it is possible to shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere as gravitation is independent of the medium.
An astronaut inside a small spaceship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
When the size of the space station orbiting around the earth is large, the astronaut will experience variation and this is because of acceleration due to gravity.
The gravitational force between a hollow spherical shell and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.
R is the radius of the spherical shell and r is the distance between m and M. M is the mass of the hollow spherical shell and m is the mass of the point. We know that,
F = GMm/r2
When the F = 0, F = GM/r2 for r ≥ R
Below is the graph which shows the variation of F versus r such that when force is maximum, r tends to infinity.
Out of aphelion and perihelion, where is the speed of the earth more and why?
According to Kepler’s second law, a real velocity is constant and is given as:
rp × vp = rA × vA
rA/rp = vp/vA
rA > rp and vp > vA
What is the angle between the equatorial plane and the orbital plane of
a) polar satellite?
b) geostationary satellite?
a) The angle between the equatorial plane and the orbital plane of the polar satellite is 90o
b) The angle between the equatorial plane and the orbital plane of a geostationary satellite is 0o
Mean solar day is the time interval between two successive noon when the sun passes through the zenith point. The sidereal day is the time interval between two successive transits of a distant star through the zenith point. Drawing the appropriate diagram showing earth’s spin and orbital motion, show that the mean solar day is four minutes longer than the sidereal day. In other words, distant stars would rise 4 minutes early every successive day.
E and E’ is the polar axis of the earth and its movement.
P’ is the translational motion
In every 24 hours, the orbit of the earth is approximately advanced by 1o
Therefore, time taken for transverse is = (24/360o) (1o) = 239.3 sec = 4 minutes.
Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in a stable equilibrium or unstable equilibrium? Give a reason for your answer.
M is the mass of the spheres and R is the radius of the spheres.
P is the midpoint of A and B.
The magnitude of the force is given as:
F1 = F2 = GMm/(5R)2
The equilibrium will be unstable as the resultant force acting on the object moves towards sphere A.
Show the nature of the following graph for a satellite orbiting the earth.
a) KE vs orbital radius R
b) PE vs orbital radius R
c) TE vs orbital radius R
a) K = 1/2mv2 = (1/2 m)(GM/R)
b) PE of satellite is U = -GMm/R = -2K
c) Total energy of the satellite = -GMm/2R