1
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $$\alpha$$W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2$$\sqrt 2$$)W. Which of the following statement(s) is(are) correct?

A
The vertical component of reaction force at O does not depend on $$\alpha$$
B
The horizontal component of reaction force at O is equal to W for $$\alpha$$ = 0.5
C
The tension in the rope is 2W for $$\alpha$$ = 0.5
D
The rope breaks if $$\alpha$$ > 1.5
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = $$-$$l, y = $$-$$h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s2 along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $$\overrightarrow L$$ and $$\overrightarrow \tau$$ respectively. $$\widehat i$$, $$\widehat j$$ and $$\widehat k$$ are unit vectors along the positive x, y and z-directions, respectively. If $$\widehat k$$ = $$\widehat i$$ $$\times$$ $$\widehat j$$ then which of the following statement(s) is(are) correct?
A
The particle arrives at the point (x = l, y = $$-$$h) at time t = 2 s
B
$$\overrightarrow \tau = 2\widehat k$$ when the particle passes through the point (x = l, y = $$-$$h)
C
$$\overrightarrow L = 4\widehat k$$ when the particle passes through the point (x = l, y = $$-$$h)
D
$$\overrightarrow \tau = \widehat k$$ when the particle passes through the point (x = 0, y = $$-$$h)
3
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+3
-0.75
A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0. It collides elastically with a rigid wall. After this collision,
A
the speed of the particle when it returns to its equilibrium position is u0.
B
the time at which the particle passes through the equilibrium position for the first time is $$t = \pi \sqrt {{m \over k}}$$
C
the time at which the maximum compression of the spring occurs is $$t = {{4\pi } \over 3}\sqrt {{m \over k}}$$
D
the time at which the particle passes through the equilibrium position for the second time is $$t = {{5\pi } \over 3}\sqrt {{m \over k}}$$
4
IIT-JEE 2010 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0.75
A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms−1. Which of the following statement(s) is (are) correct for the system of these two masses?
A
Total momentum of the system is 3 kg ms−1
B
Momentum of 5 kg mass after collision is 4 kg ms−1
C
Kinetic energy of the centre of mass is 0.75 J
D
Total kinetic energy of the system is 4 J
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