1
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $$\mu$$. If the distance of the coin from the center of the disc is $$r$$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

A
$$\sqrt{\frac{r}{\mu g}}$$
B
$$\sqrt{\frac{\mu g}{r}}$$
C
$$\frac{\mu g}{r}$$
D
$$\frac{\mu}{\sqrt{r g}}$$
2
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

A stone of mass $$900 \mathrm{~g}$$ is tied to a string and moved in a vertical circle of radius $$1 \mathrm{~m}$$ making $$10 \mathrm{~rpm}$$. The tension in the string, when the stone is at the lowest point is (if $$\pi^2=9.8$$ and $$g=9.8 \mathrm{~m} / \mathrm{s}^2$$) :

A
17.8 N
B
97 N
C
9.8 N
D
8.82 N
3
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

If the radius of curvature of the path of two particles of same mass are in the ratio $$3: 4$$, then in order to have constant centripetal force, their velocities will be in the ratio of :

A
$$1: \sqrt{3}$$
B
$$2: \sqrt{3}$$
C
$$\sqrt{3}: 2$$
D
$$\sqrt{3}: 1$$
4
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1

A train is moving with a speed of $$12 \mathrm{~m} / \mathrm{s}$$ on rails which are $$1.5 \mathrm{~m}$$ apart. To negotiate a curve radius $$400 \mathrm{~m}$$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $$g=10 \mathrm{~m} / \mathrm{s}^2)$$ :

A
6.0 cm
B
5.4 cm
C
4.8 cm
D
4.2 cm
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