1
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

Let $$f:( - 1,1) \to R$$ be such that $$f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}$$ for $$\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)$$. Then the value(s) of $$f\left( {{1 \over 3}} \right)$$ is(are)

A
$$1 - \sqrt {{3 \over 2}} $$
B
$$1 + \sqrt {{3 \over 2}} $$
C
$$1 - \sqrt {{2 \over 3}} $$
D
$$1 + \sqrt {{2 \over 3}} $$
2
IIT-JEE 2012 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0.75
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega $$. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by
IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 53 English
A
IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 53 English Option 1
B
IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 53 English Option 2
C
IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 53 English Option 3
D
IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 53 English Option 4
3
IIT-JEE 2012 Paper 2 Offline
MCQ (Single Correct Answer)
+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

IIT-JEE 2012 Paper 2 Offline Physics - Rotational Motion Question 52 English
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.
4
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.
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