270513
The ratio of escape velocities of two planets if g value on the two planets are \(9.9 \mathrm{~m} / \mathrm{s}^{2}\) and \(3.3 \mathrm{~m} / \mathrm{s}^{2}\) and their radii are \(6400 \mathrm{~km}\) and \(3200 \mathrm{~km}\) respectively is
1 \(2.36: 1\)
2 \(1.36: 1\)
3 \(3.36: 1\)
4 \(4.36: 1\)
Explanation:
\(V_{e}=\sqrt{2 g R} \Rightarrow V_{e} \propto \sqrt{g R}\)
Gravitation
270514
The escape velocity from the surface of the earth of radius \(R\) and density \(\rho\)
1 \(2 R \sqrt{\frac{2 \pi \rho G}{3}}\)
2 \(2 \sqrt{\frac{2 \pi \rho G}{3}}\)
3 \(2 \pi \sqrt{\frac{R}{g}}\)
4 \(\sqrt{\frac{2 \pi G \rho}{R^{2}}}\)
Explanation:
\(V_{e}=\sqrt{\frac{2 G M}{R}}\) but \(M=\frac{4}{3} \pi R^{3} \rho\)
Gravitation
270515
A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is
1 \(1: 1\)
2 \(1: 2\)
3 \(1: 3\)
4 \(1: 4\)
Explanation:
\(h=\frac{R}{n^{2}-1}\) Here \(n=2\)
Gravitation
270516
A spaceship is launched in to a circular orbit of radius ' \(R\) ' close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is ( \(\mathrm{g}=\) acceleration due to gravity)
1 \(1.414 \mathrm{Rg}\)
2 \(1.414 \sqrt{\operatorname{Rg}}\)
3 \(0.414 \mathrm{Rg}\)
4 \(0.414 \sqrt{g R}\)
Explanation:
\(V=V_{e}-V_{0}=\sqrt{2 g R}-\sqrt{g R}=\sqrt{g R}(\sqrt{2}-1)\)
Gravitation
270517
The escape velocity from the earth is \(11 \mathrm{~km} /\) \(\mathrm{s}\). The escape velocity from a planet having twice the radius and same density as that of the earth is (in \(\mathbf{~ k m} / \mathrm{sec}\) )
270513
The ratio of escape velocities of two planets if g value on the two planets are \(9.9 \mathrm{~m} / \mathrm{s}^{2}\) and \(3.3 \mathrm{~m} / \mathrm{s}^{2}\) and their radii are \(6400 \mathrm{~km}\) and \(3200 \mathrm{~km}\) respectively is
1 \(2.36: 1\)
2 \(1.36: 1\)
3 \(3.36: 1\)
4 \(4.36: 1\)
Explanation:
\(V_{e}=\sqrt{2 g R} \Rightarrow V_{e} \propto \sqrt{g R}\)
Gravitation
270514
The escape velocity from the surface of the earth of radius \(R\) and density \(\rho\)
1 \(2 R \sqrt{\frac{2 \pi \rho G}{3}}\)
2 \(2 \sqrt{\frac{2 \pi \rho G}{3}}\)
3 \(2 \pi \sqrt{\frac{R}{g}}\)
4 \(\sqrt{\frac{2 \pi G \rho}{R^{2}}}\)
Explanation:
\(V_{e}=\sqrt{\frac{2 G M}{R}}\) but \(M=\frac{4}{3} \pi R^{3} \rho\)
Gravitation
270515
A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is
1 \(1: 1\)
2 \(1: 2\)
3 \(1: 3\)
4 \(1: 4\)
Explanation:
\(h=\frac{R}{n^{2}-1}\) Here \(n=2\)
Gravitation
270516
A spaceship is launched in to a circular orbit of radius ' \(R\) ' close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is ( \(\mathrm{g}=\) acceleration due to gravity)
1 \(1.414 \mathrm{Rg}\)
2 \(1.414 \sqrt{\operatorname{Rg}}\)
3 \(0.414 \mathrm{Rg}\)
4 \(0.414 \sqrt{g R}\)
Explanation:
\(V=V_{e}-V_{0}=\sqrt{2 g R}-\sqrt{g R}=\sqrt{g R}(\sqrt{2}-1)\)
Gravitation
270517
The escape velocity from the earth is \(11 \mathrm{~km} /\) \(\mathrm{s}\). The escape velocity from a planet having twice the radius and same density as that of the earth is (in \(\mathbf{~ k m} / \mathrm{sec}\) )
270513
The ratio of escape velocities of two planets if g value on the two planets are \(9.9 \mathrm{~m} / \mathrm{s}^{2}\) and \(3.3 \mathrm{~m} / \mathrm{s}^{2}\) and their radii are \(6400 \mathrm{~km}\) and \(3200 \mathrm{~km}\) respectively is
1 \(2.36: 1\)
2 \(1.36: 1\)
3 \(3.36: 1\)
4 \(4.36: 1\)
Explanation:
\(V_{e}=\sqrt{2 g R} \Rightarrow V_{e} \propto \sqrt{g R}\)
Gravitation
270514
The escape velocity from the surface of the earth of radius \(R\) and density \(\rho\)
1 \(2 R \sqrt{\frac{2 \pi \rho G}{3}}\)
2 \(2 \sqrt{\frac{2 \pi \rho G}{3}}\)
3 \(2 \pi \sqrt{\frac{R}{g}}\)
4 \(\sqrt{\frac{2 \pi G \rho}{R^{2}}}\)
Explanation:
\(V_{e}=\sqrt{\frac{2 G M}{R}}\) but \(M=\frac{4}{3} \pi R^{3} \rho\)
Gravitation
270515
A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is
1 \(1: 1\)
2 \(1: 2\)
3 \(1: 3\)
4 \(1: 4\)
Explanation:
\(h=\frac{R}{n^{2}-1}\) Here \(n=2\)
Gravitation
270516
A spaceship is launched in to a circular orbit of radius ' \(R\) ' close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is ( \(\mathrm{g}=\) acceleration due to gravity)
1 \(1.414 \mathrm{Rg}\)
2 \(1.414 \sqrt{\operatorname{Rg}}\)
3 \(0.414 \mathrm{Rg}\)
4 \(0.414 \sqrt{g R}\)
Explanation:
\(V=V_{e}-V_{0}=\sqrt{2 g R}-\sqrt{g R}=\sqrt{g R}(\sqrt{2}-1)\)
Gravitation
270517
The escape velocity from the earth is \(11 \mathrm{~km} /\) \(\mathrm{s}\). The escape velocity from a planet having twice the radius and same density as that of the earth is (in \(\mathbf{~ k m} / \mathrm{sec}\) )
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Gravitation
270513
The ratio of escape velocities of two planets if g value on the two planets are \(9.9 \mathrm{~m} / \mathrm{s}^{2}\) and \(3.3 \mathrm{~m} / \mathrm{s}^{2}\) and their radii are \(6400 \mathrm{~km}\) and \(3200 \mathrm{~km}\) respectively is
1 \(2.36: 1\)
2 \(1.36: 1\)
3 \(3.36: 1\)
4 \(4.36: 1\)
Explanation:
\(V_{e}=\sqrt{2 g R} \Rightarrow V_{e} \propto \sqrt{g R}\)
Gravitation
270514
The escape velocity from the surface of the earth of radius \(R\) and density \(\rho\)
1 \(2 R \sqrt{\frac{2 \pi \rho G}{3}}\)
2 \(2 \sqrt{\frac{2 \pi \rho G}{3}}\)
3 \(2 \pi \sqrt{\frac{R}{g}}\)
4 \(\sqrt{\frac{2 \pi G \rho}{R^{2}}}\)
Explanation:
\(V_{e}=\sqrt{\frac{2 G M}{R}}\) but \(M=\frac{4}{3} \pi R^{3} \rho\)
Gravitation
270515
A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is
1 \(1: 1\)
2 \(1: 2\)
3 \(1: 3\)
4 \(1: 4\)
Explanation:
\(h=\frac{R}{n^{2}-1}\) Here \(n=2\)
Gravitation
270516
A spaceship is launched in to a circular orbit of radius ' \(R\) ' close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is ( \(\mathrm{g}=\) acceleration due to gravity)
1 \(1.414 \mathrm{Rg}\)
2 \(1.414 \sqrt{\operatorname{Rg}}\)
3 \(0.414 \mathrm{Rg}\)
4 \(0.414 \sqrt{g R}\)
Explanation:
\(V=V_{e}-V_{0}=\sqrt{2 g R}-\sqrt{g R}=\sqrt{g R}(\sqrt{2}-1)\)
Gravitation
270517
The escape velocity from the earth is \(11 \mathrm{~km} /\) \(\mathrm{s}\). The escape velocity from a planet having twice the radius and same density as that of the earth is (in \(\mathbf{~ k m} / \mathrm{sec}\) )
270513
The ratio of escape velocities of two planets if g value on the two planets are \(9.9 \mathrm{~m} / \mathrm{s}^{2}\) and \(3.3 \mathrm{~m} / \mathrm{s}^{2}\) and their radii are \(6400 \mathrm{~km}\) and \(3200 \mathrm{~km}\) respectively is
1 \(2.36: 1\)
2 \(1.36: 1\)
3 \(3.36: 1\)
4 \(4.36: 1\)
Explanation:
\(V_{e}=\sqrt{2 g R} \Rightarrow V_{e} \propto \sqrt{g R}\)
Gravitation
270514
The escape velocity from the surface of the earth of radius \(R\) and density \(\rho\)
1 \(2 R \sqrt{\frac{2 \pi \rho G}{3}}\)
2 \(2 \sqrt{\frac{2 \pi \rho G}{3}}\)
3 \(2 \pi \sqrt{\frac{R}{g}}\)
4 \(\sqrt{\frac{2 \pi G \rho}{R^{2}}}\)
Explanation:
\(V_{e}=\sqrt{\frac{2 G M}{R}}\) but \(M=\frac{4}{3} \pi R^{3} \rho\)
Gravitation
270515
A body is projected vertically up from surface of the earth with a velocity half of escape velocity. The ratio of its maximum height of ascent and radius of earth is
1 \(1: 1\)
2 \(1: 2\)
3 \(1: 3\)
4 \(1: 4\)
Explanation:
\(h=\frac{R}{n^{2}-1}\) Here \(n=2\)
Gravitation
270516
A spaceship is launched in to a circular orbit of radius ' \(R\) ' close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is ( \(\mathrm{g}=\) acceleration due to gravity)
1 \(1.414 \mathrm{Rg}\)
2 \(1.414 \sqrt{\operatorname{Rg}}\)
3 \(0.414 \mathrm{Rg}\)
4 \(0.414 \sqrt{g R}\)
Explanation:
\(V=V_{e}-V_{0}=\sqrt{2 g R}-\sqrt{g R}=\sqrt{g R}(\sqrt{2}-1)\)
Gravitation
270517
The escape velocity from the earth is \(11 \mathrm{~km} /\) \(\mathrm{s}\). The escape velocity from a planet having twice the radius and same density as that of the earth is (in \(\mathbf{~ k m} / \mathrm{sec}\) )