1
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $$\mathrm{3 R}$$ above earth surface. Where $$\mathrm{R}$$ is Radius of earth (Take $$\mathrm{R}=6400 \mathrm{~km}$$ ). The depth $$\mathrm{d}$$ is equal to

A
5260 km
B
2560 km
C
640 km
D
4800 km
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1
An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be
A
$\sqrt{\frac{g R}{2}}$
B
$\sqrt{g R}$
C
$\sqrt{2 g R}$
D
$2 \sqrt{g R}$
3
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

If the gravitational field in the space is given as $$\left(-\frac{K}{r^{2}}\right)$$. Taking the reference point to be at $$\mathrm{r}=2 \mathrm{~cm}$$ with gravitational potential $$\mathrm{V}=10 \mathrm{~J} / \mathrm{kg}$$. Find the gravitational potential at $$\mathrm{r}=3 \mathrm{~cm}$$ in SI unit (Given, that $$\mathrm{K}=6 \mathrm{~Jcm} / \mathrm{kg}$$)

A
9
B
11
C
10
D
12
4
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

A
12 hours
B
3 hours
C
6 hours
D
4 hours
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