1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

An object of mass $$1 \mathrm{~kg}$$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ]

A
48 MJ
B
24 MJ
C
36 MJ
D
12 MJ
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is -

(consider radius of earth $$R_{E}=6400 \mathrm{~km}$$ and $$\mathrm{g}$$ on earth $$10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A
1200 km
B
1600 km
C
3200 km
D
4800 km
3
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

If the radius of earth shrinks by $$2 \%$$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

A
decrease by $$2 \%$$
B
decrease by $$4 \%$$
C
increase by $$2 \%$$
D
increase by $$4 \%$$
4
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

A body of mass $$\mathrm{m}$$ is projected with velocity $$\lambda \,v_{\mathrm{e}}$$ in vertically upward direction from the surface of the earth into space. It is given that $$v_{\mathrm{e}}$$ is escape velocity and $$\lambda<1$$. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :

A
$$\frac{\mathrm{R}}{1+\lambda^{2}}$$
B
$$\frac{R}{1-\lambda^{2}}$$
C
$$\frac{R}{1-\lambda}$$
D
$$\frac{\lambda^{2} \mathrm{R}}{1-\lambda^{2}}$$
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