1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be -

A
$${g \over {13l}}$$
B
$${g \over {2l}}$$
C
$${g \over {3l}}$$
D
$${7g \over {3l}}$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - (g = 10 ms–2)
A
30 m
B
40 m
C
20 m
D
10 m
3
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
Two masses m and $${m \over 2}$$ are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is $$\tau$$ = k$$\theta$$ for angular displacement $$\theta$$. If the rod is rotated by $$\theta$$0 and released, the tension in it when it passes through its mean position will be :

A
$${{3k{\theta _0}^2} \over l}$$
B
$${{2k{\theta _0}^2} \over l}$$
C
$${{k{\theta _0}^2} \over l}$$
D
$${{k{\theta _0}^2} \over {2l}}$$
4
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A force of $$40$$ $$N$$ acts on a point $$B$$ at the end of an $$L$$-shaped object, as shown in the figure. The angle $$\theta$$ that will produce maximum moment of the force about point $$A$$ is given by :

A
$$\tan \theta = {1 \over 2}$$
B
$$\tan \theta = 2$$
C
$$\tan \theta = 4$$
D
$$\tan \theta = {1 \over 4}$$
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