1
IIT-JEE 2012 Paper 2 Offline
+3
-0.75
Consider a disc rotating in the horizontal plane with a constant angular speed $$\omega$$ about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y - z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $${1 \over 8}$$ rotation, (ii) their range is less than half the disc radius, and (iii) $$\omega$$ remains constant throughout. Then

A
P lands in the shaded region and Q in the unshaded region.
B
P lands in the unshaded region and Q in the shaded region.
C
Both P and Q land in the unshaded region.
D
Both P and Q land in the shaded region.
2
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
A
Both cylinders P and Q reach the ground at the same time.
B
Cylinders P has larger linear acceleration than cylinder Q.
C
Both cylinders reach the ground with same translational kinetic energy.
D
Cylinder Q reaches the ground with larger angular speed.
3
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $$\omega$$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $${\omega \over 2}$$. The ring and disc are separated by frictionless ball bearings. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of $$30^\circ$$ with the horizontal. Then with respect to the horizontal surface,
A
the point O has linear velocity $$3R\omega \widehat i$$
B
the point P has linear velocity $${{11} \over 4}R\omega \widehat i + {{\sqrt 3 } \over 4}R\omega \widehat k$$
C
the point P has linear velocity $${{13} \over 4}R\omega \widehat i - {{\sqrt 3 } \over 4}R\omega \widehat k$$
D
the point P has linear velocity $$\left( {3 - {{\sqrt 3 } \over 4}} \right)R\omega \widehat i + {1 \over 4}R\omega \widehat k$$
4
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Two spherical planets P and Q have the same uniform density r, masses MP and MQ and surface areas A and 4A respectively. A spherical planet R also has uniform density r and its mass is (MP + MQ). The escape velocities from the planets P, Q and R are VP, VQ and VR, respectively. Then
A
VQ > VR > VP
B
VR > VQ > VP
C
$${{{V_R}} \over {{V_P}}} = 3$$
D
$${{{V_P}} \over {{V_Q}}} = {1 \over 2}$$
2023
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
EXAM MAP
Joint Entrance Examination