Gravitation

MCQs (Part - IX)

Question 41: In a hypothetical concept, electron of mass me revolveds around nucleus due to gravitational force of attraction between electron and proton of mass mp. If the radius of circular path of electron is r then the speed of electron is:

  4. none of these

Answer: (c)

Explanation The force of attraction between electron and proton provides required centripetal force.

or

Question 42: Theree point masses each of mass m rotate in a circle of radius r with constant angular velocity w due to their mutual gravitational attraction. If at any instant, the masses are on the vertex of an equilateral triangle of side a, then the value of w is:

  4. none of these

Answer: (b)

Explanation:

Here,

F = 2F0 cos 30º

or

or

Question 43: A spherical mass of radius is taken out from a uniform sphere of radius R and mass density r. The force which this sphere having a cavity will exert on a mass m placed at a distance of x from its centre x (x < R) is:

  4. none of these

Answer: (b)

Explanation: The force due to whole sphere is

The force due to small cutting portion is

The net force is

F = F1 - F2

Question 44: Suppose the gravitational force varies inversely as the nth power of the distance. then the time period of a planet in circular orbit of radius R anound the sun will be proportional to:

  1. R n
  2. R (n + 1) /2
  3. R (n _ 1) /2
  4. R -n

Answer: (b) R (n + 1) /2

Question 45: A straight rod of length L extends from x = a to x = L + a. The gravitational force exeerted by it on a point mass m at x = 0 if the linear density of rod is m = A + Bx2, is:

Answer: (b)

Explanation






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