1
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

As shown in the figure, a particle is moving with constant speed $$\pi ~\mathrm{m} / \mathrm{s}$$. Considering its motion from $$\mathrm{A}$$ to $$\mathrm{B}$$, the magnitude of the average velocity is :

A
$$\pi ~\mathrm{m} / \mathrm{s}$$
B
$$1.5 \sqrt{3} \mathrm{~m} / \mathrm{s}$$
C
$$\sqrt{3} \mathrm{~m} / \mathrm{s}$$
D
$$2 \sqrt{3} \mathrm{~m} / \mathrm{s}$$
2
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

A child of mass $$5 \mathrm{~kg}$$ is going round a merry-go-round that makes 1 rotation in $$3.14 \mathrm{~s}$$. The radius of the merry-go-round is $$2 \mathrm{~m}$$. The centrifugal force on the child will be

A
50 N
B
80 N
C
100 N
D
40 N
3
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

A particle is moving with constant speed in a circular path. When the particle turns by an angle $$90^{\circ}$$, the ratio of instantaneous velocity to its average velocity is $$\pi: x \sqrt{2}$$. The value of $$x$$ will be -

A
1
B
7
C
5
D
2
4
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

A small block of mass $$100 \mathrm{~g}$$ is tied to a spring of spring constant $$7.5 \mathrm{~N} / \mathrm{m}$$ and length $$20 \mathrm{~cm}$$. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $$5 ~\mathrm{rad} / \mathrm{s}$$ about point $$\mathrm{A}$$, then tension in the spring is -

A
0.50 N
B
1.5 N
C
0.75 N
D
0.25 N
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