SATHEE: Gravitation - Result Question 54

Gravitation - Result Question 54

57. The escape velocity from earth is $11.2 k m / s$ . If a body is to be projected in a direction making an angle $45^{\circ}$ to the vertical, then the escape velocity is

[1993]

(a) $11.2 \times 2 k m / s$

(b) $11.2 k m / s$

(d) $11.2 \sqrt{2} k m / s$

Show Answer

Answer:

Correct Answer: 57. (b)

Solution:

(b) Escape velocity does not depend on the angle of projection.

The value of escape velocity is given by

$V_{e} = \sqrt{\frac{2 G M}{R}}$

Here, $M =$ mass of earth, $G =$ gravitational constant $R =$ radius of earth

$\begin{aligned} V_{e} & = \sqrt{\frac{2 G M}{R^{2}}} \\ = \sqrt{\frac{2 \times G}{R^{2}} \times \frac{4}{3} π R^{3} ρ} (∵ M = \frac{4}{3} π R^{3} ρ) \\ V_{e} & = R \sqrt{\frac{8 π G ρ}{3}} \end{aligned}$

Thus, value of escape velocity depends upon the mass $M$ , density $ρ$ and radius $R$ of earth/planet from which the body is projected and independent of angle of projection.

Gravitation - Result Question 54

57. The escape velocity from earth is $11.2 k m / s$ . If a body is to be projected in a direction making an angle $45^{\circ}$ to the vertical, then the escape velocity is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Gravitation - Result Question 54

57. The escape velocity from earth is 11.2km/s. If a body is to be projected in a direction making an angle 45∘ to the vertical, then the escape velocity is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

57. The escape velocity from earth is $11.2 k m / s$ . If a body is to be projected in a direction making an angle $45^{\circ}$ to the vertical, then the escape velocity is