1
AIPMT 2011 Mains
+4
-1
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 Mains
+4
-1
A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :
A
$${{GM} \over a}$$
B
$${{2GM} \over a}$$
C
$${{3GM} \over a}$$
D
$${{4GM} \over a}$$
3
AIPMT 2011 Prelims
+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
4
AIPMT 2010 Mains
+4
-1
The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R2(R2 > R1) is
A
GmM $$\left( {{1 \over {R_1^2}} - {1 \over {R_2^2}}} \right)$$
B
GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
C
2GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
D
$${1 \over 2}$$GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
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