Escape velocity on a planet is ve. If radius of the planet remains same and mass becomes 4 times, the escape velocity becomes
(A) 4ve
(B) 2ve
(C) ve
(D) 0.5 ve
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Assuming that a planet goes round the sun in a circular orbit of radius `0.5AU` determine the angle of maximum elongation for the planet and its dista
Correct Answer - `30^(@), 0.866AU`
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Time period of revolution of a satellite around a planet of radius R is T. Period of revolution around another planet whose radius is 3R is
Correct option is: (A) T Period of resolution \(T = 2 \pi \sqrt \frac{R^3}{GM} \) \(T = 2 \pi \sqrt \frac{R^3}{G \frac{4}{3} \pi R^3 \rho} \) The period of revolution depends upon the density of...
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Time period of revolution of a satellite around a planet of radius R is T. Period of revolution around another planet whose radius is 3R is
2 Answers
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Escape velocity on a planet is ve. If radius of the planet remains same and mass becomes 4 times, the escape velocity becomes
2 Answers
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If the escape velocity of a body on Earth is 11.2 km/s, the escape velocity of the body thrown at an angle 45° with the horizontal will be
Correct option is: (A) 11.2 km/s Escape velocity does not depend on the angle of projection. \(V_{escape} = \sqrt {2gRe} \)
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If the escape velocity of a body on Earth is 11.2 km/s, the escape velocity of the body thrown at an angle 45° with the horizontal will be
2 Answers
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If ve and vo represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R respectively, then
Correct option is: (B) \(\sqrt{2}\)vo = ve
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Two coins are tossed 400 times and we get two heads : 112 times, one head , 160 times , 0 head , 128 times . When two coins are tossed at random , wha
Correct Answer - (i) 0.28 (ii) 0.4 (iii) 0.32
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Consider a particle of mass \( m \) having linear momentum \( P \) at position \( r \) relative to the origin \( O \). Which of the following equations correctly relates \( r , P , L \) ? a) \( \left[\left(\frac{d L}{d t}\right)+r x\left(\frac{d P}{d t}\right)\right]=0 \) b) \( \left[\left(\frac{d L}{d t}\right)-r x\left(\frac{d P}{d t}\right)\right]=0 \) c) \( \left[\left(\frac{d L}{d t}\right) \times\left(\frac{d r}{d t}\right) \times P\right]=0 \) d) \( \left[\left(\frac{d L}{d t}\right)-\left(\frac{d r}{d t}\right) \times P\right]=0 \)
Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)
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Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \). Which one of the following is correct ? [IIT-2007] (a) \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}=\overrightarrow{0} \) (b) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ c } \times \overrightarrow{ a } \neq \overrightarrow{0} \) (c) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ a } \times \overrightarrow{ c } \neq \overrightarrow{0} \) (d) \( \vec{a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a} \) are mutually \( \perp \)
Given that \(\vec a, \vec b\) and \(\vec c\)are unit vectors. i.e., |\(\vec a\)| = |\(\vec b\)| = |\(\vec c\)| = 1 And \(\vec a\) + \(\vec b\) + \(\vec c\) = \(\vec 0\) Then \((\vec a+\vec b+\vec c).(\vec a+\vec b+\vec c)=\vec 0.\vec...
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