A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $$\theta$$. Which of the following statements about its motion is/are correct?
A
Instantaneous torque about the point in contact with the floor is proportional to sin$$\theta$$
B
The trajectory of the point A is parabola
C
The mid-point of the bar will fall vertically downward
D
When the bar makes an angle $$\theta$$ with the vertical, the displacement of its mid-point from the initial position is proportional to (1 $$-$$ cos$$\theta$$)
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A block of mass $$M$$ has a circular cut with a frictionless surface as shown. The block resets on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $$x=0,$$ in a co-ordinate system fixed to the table. A point mass $$m$$ is released from rest at the topmost point of the path as shown and it slides down.
When the mass loses contact with the block, its position is $$x$$ and the velocity is $$v.$$ At that instant, which of the following options is/are correct?
A
The position of the point mass $$m$$ is :
$$x = - \sqrt 2 {{mR} \over {M + m}}$$
B
The velocity of the point mass $$m$$ is :
$$v = \sqrt {{{2gR} \over {1 + {m \over M}}}} $$
C
The $$x$$ component of displacement of the center
of mass of the block $$M$$ is: $$ - {{mR} \over {M + m}}$$
D
The velocity of the block $$M$$ is:
$$V = - {m \over M}\sqrt {2gR} $$
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a
massless, rigid rod of length $$l = \sqrt {24} a$$ through their centers. This assembly is laid on a firm and flat
surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is $$\omega $$. The angular momentum of the entire assembly about the point ‘O’ is $$\overrightarrow L $$ (see the figure). Which of the following statement(s) is(are) true?
A
The center of mass of the assembly rotates about the z-axis with an angular speed of $${\omega \over 5}$$
B
The magnitude of angular momentum of center of mass of the assembly about the point O is $$81\,m{a^2}\omega $$
C
The magnitude of angular momentum of the assembly about its center of mass is $${{17m{a^2}\omega } \over 2}$$
D
The magnitude of the z-component of $$\overrightarrow L $$
is $$55m{a^2}\omega $$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
The position vector $$\overrightarrow r $$ of a particle of mass m is given by the following equation
$$$\overrightarrow r \left( t \right) = \alpha {t^3}\widehat i + \beta {t^2}\widehat j,$$$where $$\alpha = {{10} \over 3}m{s^{ - 3}}$$, $$\beta = 5\,m{s^{ - 2}}$$ and m = 0.1 kg. At t = 1 s, which of the following
statement(s) is(are) true about the particle?
A
The velocity $$\overrightarrow v $$ is given by $$\overrightarrow v = \left( {10\widehat i + 10\widehat j} \right)$$ ms-1
B
The angular momentum $$\overrightarrow L $$
with respect to the origin is given by $$\overrightarrow L = - \left( {{5 \over 3}} \right)\widehat k\,N\,m\,s$$
C
The force $$\overrightarrow F $$
is given by $$\overrightarrow F = \left( {\widehat i + 2\widehat j} \right)N$$
D
The torque $$\overrightarrow \tau $$ with respect to the origin is given by $$\overrightarrow \tau = - \left( {{{20} \over 3}} \right)\widehat k\,N\,m$$
