1
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
$$\frac{\lambda^{2} \mathrm{R}}{1-\lambda^{2}}$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$, having masses in the ratio $$4: 3$$, are revolving in circular orbits of radii $$3 \mathrm{r}$$ and $$4 \mathrm{r}$$ respectively around the earth. The ratio of total mechanical energy of $$\mathrm{A}$$ to $$\mathrm{B}$$ is :

A
9 : 16
B
16 : 9
C
1 : 1
D
4 : 3
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be :

(Take radius of earth $$=6400 \mathrm{~km}$$ and $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ )

A
800 km
B
1600 km
C
2133 km
D
4800 km
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

The percentage decrease in the weight of a rocket, when taken to a height of $$32 \mathrm{~km}$$ above the surface of earth will, be :

$$($$ Radius of earth $$=6400 \mathrm{~km})$$

A
1%
B
3%
C
4%
D
0.5%
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