1
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is :
A
$${1 \over 4}{{M{L^2}} \over {{\pi ^2}}}$$
B
$${1 \over 2}{{M{L^2}} \over {{\pi ^2}}}$$
C
$${2 \over 5}{{M{L^2}} \over {{\pi ^2}}}$$
D
$${{M{L^2}} \over {{\pi ^2}}}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :

[The coefficient of static friction, $$\mu$$s' is 0.4]
A
0
B
5 mg
C
$${7 \over 2}$$ mg
D
$${{mg} \over 5}$$
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $$\omega$$. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :
A
$$\omega {M \over {M + m}}$$
B
$$\omega {{M + 2m} \over M}$$
C
$$\omega {M \over {M + 2m}}$$
D
$$\omega {{M - 2m} \over {M + 2m}}$$
4
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
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