1
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Consider a body of mass $$1.0$$ $$kg$$ at rest at the origin at time $$t=0.$$ A force $$\overrightarrow F = \left( {\alpha t \widehat i + \beta \widehat j} \right)$$ is applied on the body, where $$\alpha = 1.0N{s^{ - 1}}$$ and $$\beta = 1.0\,N.$$ The torque acting on the body about the origin at time $$t=1.0s$$ is $$\overrightarrow \tau .$$ Which of the following statements is (are) true?
A
$$\left| {\overrightarrow \tau } \right| = {1 \over 3}\,Nm$$
B
The torque $$\overrightarrow \tau$$ is in the direction of the unit vector $$+ \,\widehat k$$
C
The velocity of the body at $$t = 1s$$ is $$\overrightarrow v = {1 \over 2}\left( {\widehat i + 2\widehat j} \right)m{s^{ - 1}}$$
D
The magnitude of displacement of the body at $$t = 1s$$ is $${1 \over 6}m$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $$\tau$$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct? A
If the force is applied normal to the circumference at point P, then $$\tau$$ is zero
B
If the force is applied tangentially at point S, then $$\tau$$ $$\ne$$ 0 but the wheel never climbs the step
C
If the force is applied at point P tangentially, then $$\tau$$ decreases continuously as the wheel climbs
D
If the force is applied normal to the circumference at point X, then $$\tau$$ is constant
3
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
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$$\theta$$)
4
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:

$$V = - {m \over M}\sqrt {2gR}$$
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