1
JEE Main 2024 (Online) 1st February Evening Shift
+4
-1
A disc of radius $\mathrm{R}$ and mass $\mathrm{M}$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

A
$\frac{3}{4} \frac{v^2}{\mathrm{~g}}$
B
$\frac{v^2}{g}$
C
$\frac{2}{3} \frac{v^2}{\mathrm{~g}}$
D
$\frac{1}{2} \frac{v^2}{\mathrm{~g}}$
2
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

A particle of mass $$\mathrm{m}$$ is projected with a velocity '$$\mathrm{u}$$' making an angle of $$30^{\circ}$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $$\mathrm{h}$$ is :

A
$$\frac{\mathrm{mu}^3}{\sqrt{2} \mathrm{~g}}$$
B
zero
C
$$\frac{\sqrt{3}}{2} \frac{\mathrm{mu}^2}{\mathrm{~g}}$$
D
$$\frac{\sqrt{3}}{16} \frac{\mathrm{mu}^3}{\mathrm{~g}}$$
3
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

A heavy iron bar of weight $$12 \mathrm{~kg}$$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $$60^{\circ}$$ with the horizontal, the weight experienced by the man is :

A
$$3 \mathrm{~kg}$$
B
$$6 \mathrm{~kg}$$
C
$$6 \sqrt{3} \mathrm{~kg}$$
D
$$12 \mathrm{~kg}$$
4
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

A disc is rolling without slipping on a surface. The radius of the disc is $$R$$. At $$t=0$$, the top most point on the disc is $$\mathrm{A}$$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

A
$$R\sqrt {({\pi ^2} + 1)}$$
B
$$2R$$
C
$$R\sqrt {({\pi ^2} + 4)}$$
D
$$2R\sqrt {(1 + 4{\pi ^2})}$$
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