1
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\mathrm{G}$$ be the gravitational constant and $$\mathrm{u}$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{\mathrm{uG}}$$ :

A
Gravitational potential
B
pressure gradient per unit mass
C
Energy per unit mass
D
Force per unit mass
2
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Match List I with List II :

LIST I LIST II
A. Kinetic energy of planet I. $$
-\mathrm{GMm} / \mathrm{a}
$$
B. Gravitation Potential energy of sun-planet system II. $$
\mathrm{GMm} / 2 \mathrm{a}
$$
C. Total mechanical energy of planet III. $$
\frac{\mathrm{Gm}}{\mathrm{r}}
$$
D. Escape energy at the surface of planet for unit mass object IV. $$
-\mathrm{GMm} / 2 \mathrm{a}
$$

(Where $$\mathrm{a}=$$ radius of planet orbit, $$\mathrm{r}=$$ radius of planet, $$\mathrm{M}=$$ mass of Sun, $$\mathrm{m}=$$ mass of planet)

Choose the correct answer from the options given below :

A
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
B
(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
C
(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
D
(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
3
JEE Main 2024 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A $$90 \mathrm{~kg}$$ body placed at $$2 \mathrm{R}$$ distance from surface of earth experiences gravitational pull of :

($$\mathrm{R}=$$ Radius of earth, $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$)

A
300 N
B
225 N
C
100 N
D
120 N
4
JEE Main 2024 (Online) 4th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Correct formula for height of a satellite from earths surface is :

A
$$\left(\frac{T^2 R^2 g}{4 \pi^2}\right)^{1 / 3}-R$$
B
$$\left(\frac{T^2 R^2 g}{4 \pi}\right)^{1 / 2}-R$$
C
$$\left(\frac{T^2 R^2 g}{4 \pi^2}\right)^{-1 / 3}+R$$
D
$$\left(\frac{T^2 R^2}{4 \pi^2 g}\right)^{1 / 3}-R$$
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