1
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$r$$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $$n^{\text {th }}$$ orbit will be proportional to,

A
$$\sqrt{n}$$
B
$$n^{2}$$
C
$$\frac{1}{n}$$
D
$$n$$
2
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The weight of a body on the surface of the earth is $$100 \mathrm{~N}$$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

A
50 N
B
64 N
C
25 N
D
100 N
4
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Choose the incorrect statement from the following:

A
The linear speed of a planet revolving around the sun remains constant.
B
When a body falls towards earth, the displacement of earth towards the body is negligible.
C
The speed of satellite in a given circular orbit remains constant.
D
For a planet revolving around the sun in an elliptical orbit, the total energy of the planet remains constant.
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