1
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

A particle is placed at the point $$A$$ of a frictionless track $$A B C$$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is :

(Take $$g=10 \mathrm{~m} / \mathrm{s}^2$$).

A
$$2 \sqrt{10} \mathrm{~m} / \mathrm{s}$$
B
$$10 \mathrm{~m} / \mathrm{s}$$
C
$$\sqrt{10} \mathrm{~m} / \mathrm{s}$$
D
$$20 \mathrm{~m} / \mathrm{s}$$
2
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

A bob of mass '$$m$$' is suspended by a light string of length '$$L$$'. It is imparted a minimum horizontal velocity at the lowest point $$A$$ such that it just completes half circle reaching the top most position B. The ratio of kinetic energies $$\frac{(K . E)_A}{(K . E)_B}$$ is :

A
5 : 1
B
3 : 2
C
1 : 5
D
2 : 5
3
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

A block of mass $$100 \mathrm{~kg}$$ slides over a distance of $$10 \mathrm{~m}$$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $$(\operatorname{in} J$$) is :

A
3900
B
4500
C
4200
D
4000
4
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

The potential energy function (in $$J$$ ) of a particle in a region of space is given as $$U=\left(2 x^2+3 y^3+2 z\right)$$. Here $$x, y$$ and $$z$$ are in meter. The magnitude of $$x$$-component of force (in $$N$$ ) acting on the particle at point $$P(1,2,3) \mathrm{m}$$ is :

A
4
B
2
C
8
D
6
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