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

A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 2t where t is in second and $$\alpha$$ is in rads$$-$$2. At t = 0, the ball has angular velocity of 10 rads$$-$$1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

A
$${3 \over 2}{t^4} - {t^2} + 10t$$
B
$${{{t^4}} \over 2} - {{{t^3}} \over 3} + 10t + 4$$
C
$${{2{t^4}} \over 3} - {{{t^3}} \over 6} + 10t + 12$$
D
$$2{t^4} - {{{t^3}} \over 2} + 5t + 4$$
2
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

A $$\sqrt {34}$$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ef and Fw are the reaction forces of the floor and the wall, then ratio of $${F_w}/{F_f}$$ will be :

(Use g = 10 m/s2.)

A
$${6 \over {\sqrt {110} }}$$
B
$${3 \over {\sqrt {113} }}$$
C
$${3 \over {\sqrt {109} }}$$
D
$${2 \over {\sqrt {109} }}$$
3
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
4
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
$${{k + m{\omega ^2}{l_0}} \over {m{\omega ^2}}}$$
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