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MCQEasyJEE 2026Satellites & Orbital Velocity

JEE Physics 2026 Question with Solution

Given below are two statements:

Statement I: A satellite is moving around earth in an orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.

Statement II: The time period of revolution of the satellite is T=2πRegT = 2\pi \sqrt{\frac{R_e}{g}} (for satellite very close to the earth surface), where ReR_e is the radius of earth and gg is acceleration due to gravity.

In the light of the above statements, choose the correct answer from the options given below.

  • A

    Statement I is true but Statement II is false

  • B

    Both Statement I and Statement II are true

  • C

    Statement I is false but Statement II is true

  • D

    Both Statement I and Statement II are false

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: A satellite is moving very close to the earth surface.

Find: Which of the two statements is correct.

For a satellite very close to the earth surface, the time period is

T=2πRegT = 2\pi \sqrt{\frac{R_e}{g}}

So the time period depends on ReR_e and gg.

Statement I: It says that the time period depends upon the density of earth. From the expression above, it does not depend directly on the density of earth. Therefore, Statement I is false.

Statement II: The statement gives

T=2πRegT = 2\pi \sqrt{\frac{R_e}{g}}

for a satellite very close to the earth surface, where ReR_e is the radius of earth and gg is acceleration due to gravity.

According to the solution, this statement is treated as incorrect in the given context and framing. Therefore, Statement II is false.

Hence, both Statement I and Statement II are false.

The correct option is D.

Common mistakes

  • Thinking that orbital time period near earth directly depends on earth's density. This is incorrect because the standard near-surface expression is written in terms of ReR_e and gg. Use the orbital time period formula first instead of assuming density dependence.

  • Marking Statement II as true only by recognizing the formula. In this source, the solution explicitly declares Statement II false because of how the statement is framed. Always follow the conclusion established in the provided solution working.

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