1
AIPMT 2011 Mains
+4
-1
A mass m moving horizontally (along the x-axis) with velocity $$v$$ collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2$$v$$. The final velocity of the combination is
A
$${3 \over 2}v\widehat i + {1 \over 4}v\widehat j$$
B
$${1 \over 4}v\widehat i + {3 \over 2}v\widehat j$$
C
$${1 \over 3}v\widehat i + {2 \over 3}v\widehat j$$
D
$${2 \over 3}v\widehat i + {1 \over 3}v\widehat j$$
2
AIPMT 2011 Mains
+4
-1
A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will A
decrease by a factor of 2
B
remain constant
C
increase by a factor of 2
D
increase by a factor of 4
3
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
$$\sqrt {2g{R^2}}$$
4
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
$${{4GM} \over a}$$
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