1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is

A
$$\sqrt {{{mv} \over K}}$$
B
$$\sqrt {{m \over {2K}}}$$
C
$$\sqrt {{{mv} \over {2K}}}$$
D
$$v\sqrt {{m \over {2K}}}$$
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
A triangular plate is shown. A force $$\overrightarrow F$$ = 4$$\widehat i$$ $$-$$ 3$$\widehat j$$ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :

A
$$-$$ 15 + 20$$\sqrt 3$$, 15 + 20$$\sqrt 3$$
B
15 $$-$$ 20$$\sqrt 3$$, 15 + 20$$\sqrt 3$$
C
15 + 20$$\sqrt 3$$, 15 $$-$$ 20$$\sqrt 3$$
D
$$-$$ 15 $$-$$ 20$$\sqrt 3$$, 15 $$-$$ 20$$\sqrt 3$$
3
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is :
(take g = 9.8 ms-2)

A
831.4 m/s
B
811.4 m/s
C
841.4 m/s
D
821.4 m/s
4
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

A
$$\sqrt 3$$ ml2
B
2 ml2
C
ml2
D
3 ml2
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