1
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is :
A
$$2\sqrt {{k \over p}}$$
B
$$2\sqrt {{p \over k}}$$
C
$$\sqrt {{{2p} \over 2}}$$
D
$$\sqrt {{{2k} \over p}}$$
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $$\times$$ 106 N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms–2 , the value of x will be close to :
A
8 cm
B
4 cm
C
40 cm
D
80 cm
3
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
4
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
$${{k{\theta _0}^2} \over {2l}}$$
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