1
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
2
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
3
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1 A stone of mass $1 \mathrm{~kg}$ is tied to end of a massless string of length $1 \mathrm{~m}$. If the breaking tension of the string is $400 \mathrm{~N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :
A
$20 \mathrm{~ms}^{-1}$
B
$40 \mathrm{~ms}^{-1}$
C
$400 \mathrm{~ms}^{-1}$
D
$10 \mathrm{~ms}^{-1}$
4
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1 A body is moving with constant speed, in a circle of radius $10 \mathrm{~m}$. The body completes one revolution in $4 \mathrm{~s}$. At the end of 3rd second, the displacement of body (in $\mathrm{m}$ ) from its starting point is :
A
$15 \pi$
B
30
C
$10 \sqrt{2}$
D
$5 \pi$
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