1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30$$^\circ$$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?

A
0.60 s
B
0.52 s
C
0.80 s
D
0.57 s
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) 17th March Morning Shift
+4
-1
A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $$\omega$$. The angular momentum of M about point A is LA which lies in the positive z direction and the angular momentum of M about point B is LB. The correct statement for this system is :

A
LA is constant, both in magnitude and direction
B
LB is constant in direction with varying magnitude
C
LB is constant, both in magnitude and direction
D
LA and LB are both constant in magnitude and direction
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be :
A
$${{2mgh} \over {I + 2m{r^2}}}$$
B
$${{2mgh} \over {I + m{r^2}}}$$
C
2gh
D
$${{2gh} \over {I + m{r^2}}}$$
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