1
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Match List-I with List-II

List-I List-II
(A) Moment of inertia of solid sphere of radius R about any tangent. (I) $${5 \over 3}M{R^2}$$
(B) Moment of inertia of hollow sphere of radius (R) about any tangent. (II) $${7 \over 5}M{R^2}$$
(C) Moment of inertia of circular ring of radius (R) about its diameter. (III) $${1 \over 4}M{R^2}$$
(D) Moment of inertia of circular disc of radius (R) about any diameter. (IV) $${1 \over 2}M{R^2}$$

Choose the correct answer from the options given below :

A
A - II, B - I, C - IV, D - III
B
A - I, B - II, C - IV, D - III
C
A - II, B - I, C - III, D - IV
D
A - I, B - II, C - III, D - IV
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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