1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1 When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

A
19.6 m
B
29.4 m
C
39.2 m
D
73.5 m
2
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1 One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $$\omega$$ about an axis passing through fixed end, then the elongation of the spring will be :

A
$${{k - m{\omega ^2}{l_0}} \over {m{\omega ^2}}}$$
B
$${{m{\omega ^2}{l_0}} \over {k + m{\omega ^2}}}$$
C
$${{m{\omega ^2}{l_0}} \over {k - m{\omega ^2}}}$$
D
$${{k + m{\omega ^2}{l_0}} \over {m{\omega ^2}}}$$
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1 A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

A
$${2 \over 5}$$
B
$${2 \over 7}$$
C
$${1 \over 5}$$
D
$${7 \over 10}$$
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1 A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads$$-$$1).

A
$${M \over {(M + m)}}$$
B
$${{(M + 2m)} \over {2M}}$$
C
$${{2M} \over {(M + 2m)}}$$
D
$${{2(M + 2m)} \over M}$$
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