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

In the given arrangement of a doubly inclined plane two blocks of masses $$M$$ and $$m$$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $$m$$, for which $$M=10 \mathrm{~kg}$$ will move down with an acceleration of $$2 \mathrm{~m} / \mathrm{s}^2$$, is: (take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\left.\tan 37^{\circ}=3 / 4\right)$$

A
4.5 kg
B
6.5 kg
C
9 kg
D
2.25 kg
2
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

A block of mass $$m$$ is placed on a surface having vertical crossection given by $$y=x^2 / 4$$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

A
1/2 m
B
1/3 m
C
1/6 m
D
1/4 m
3
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

Three blocks $$A, B$$ and $$C$$ are pulled on a horizontal smooth surface by a force of $$80 \mathrm{~N}$$ as shown in figure

The tensions T$$_1$$ and T$$_2$$ in the string are respectively :

A
40N, 64N
B
60N, 80N
C
80N, 100N
D
88N, 96N
4
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $$2 \mathrm{~kg}$$ is :

A
$$\mathrm{\frac{g}{2}}$$
B
$$\mathrm{\frac{g}{4}}$$
C
$$\mathrm{g}$$
D
$$\mathrm{\frac{g}{3}}$$
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