A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is
A
$$\sqrt {{{2GM} \over {{R^2}}}} $$
B
$$\sqrt {{{2GM} \over R}} $$
C
$$\sqrt {{{2gM} \over {{R^2}}}} $$
D
$$\sqrt {2g{R^2}} $$
2
AIPMT 2011 Prelims
MCQ (Single Correct Answer)
+4
-1
A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If $$v$$1 and $$v$$2 are the linear velocities at these points respectively, then the ratio $${{{v_1}} \over {{v_2}}}$$ is
A
(r1 /r2)2
B
r2/r1
C
(r2/r1)2
D
r1/r2
3
AIPMT 2010 Mains
MCQ (Single Correct Answer)
+4
-1
The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below
The correct figure is
A
(4)
B
(1)
C
(2)
D
(3)
4
AIPMT 2010 Mains
MCQ (Single Correct Answer)
+4
-1
(1) Centre of gravity (C.G) of a body is the point at which the weight of the body acts
(2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
(3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.
(4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis.
Which one of the following pairs of statements is correct ?
