1
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
$${{k{\theta _0}^2} \over {2l}}$$
2
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed $$\upsilon$$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically $${5 \over 6}$$th of the initial kinetic energy is lost in whole process. What is value of M/m ?

A
5
B
2
C
4
D
3
3
JEE Main 2018 (Offline)
+4
-1
In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :
A
$${{{v_0}} \over {\sqrt 2 }}$$
B
$${{v_0}} \over 4$$
C
$$\sqrt 2 {v_0}$$
D
$${{v_0}} \over 2$$
4
JEE Main 2018 (Offline)
+4
-1
The mass of a hydrogen molecule is 3.32 $$\times$$ 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly:
A
2.35 $$\times$$ 103 N m-2
B
4.70 $$\times$$ 103 N m-2
C
2.35 $$\times$$ 102 N m-2
D
4.70 $$\times$$ 102 N m-2
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