Student Login

Home›Chapters›Gravitation PYQs›Escape Velocity›Question 49

JEE Main 2021 (25 Feb, Shift 2) · Escape Velocity

Escape Velocity question from JEE Main 2021 (25 Feb, Shift 2)

Q49JEE Main 2021 · 25 FEB · SHIFT 2Medium

Escape Velocity

The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that $v_i$ $=$ $\sqrt{\frac{x}{y}} \times$ $v_e$ . The value of x will be ____________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 10

To reach $h = 10R$ (distance $11R$ ): $\frac{1}{2}v_i^2 = GM\left(\frac{1}{R} - \frac{1}{11R}\right) = \frac{GM}{R}\cdot\frac{10}{11}$ .
$v_i^2 = \frac{2GM}{R}\cdot\frac{10}{11} = \frac{10}{11}v_e^2$ .
$v_i = \sqrt{\frac{10}{11}}\,v_e$ , so $x = 10$ .
Answer: $10$ .

Report a mistake

More questions on Escape Velocity

A particle of mass ' m ' is kept at rest at a height 3R from the surface of earth, where…MHT CET 2021 (21 Sep, Shift 1)
A body is projected from earth's surface with thrice the escape velocity from the surface…MHT CET 2021 (20 Sep, Shift 2)
A body is projected vertically upwards from the surface of earth with a velocity…JEE Main 2021 (22 Jul, Shift 2)
The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their…JEE Main 2021 (31 Aug, Shift 1)
Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M…JEE Main 2021 (27 Jul, Shift 1)
The escape velocity of a body from any planet, whose mass is six times the mass of earth…MHT CET 2020 (19 Oct, Shift 2)
Planet A has mass M and radius R. Planet B has half the mass and half the radius of…JEE Main 2020 (9 Jan, Shift 2)
A body is moving in a low circular orbit about a planet of mass M and radius R. The…JEE Main 2020 (4 Sep, Shift 2)