A satellite is seen after every 6 hr over the equator of the earth. It is known that it rotates opposite to that of earth's direction. Then the angular velocity of the satellite about the centre of earth will be π/n rad/h. Find the value of n.
Physics · Mixed Chapter
JEE Mains

Question

A satellite is seen after every 6 hr over the equator of the earth. It is known that it rotates opposite to that of earth's direction. Then the angular velocity of the satellite about the centre of earth will be π/n rad/h. Find the value of n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Earth's angular speed is ωₑ=2π/24=π/12 rad/h. A retrograde satellite has angular speed opposite to Earth; their relative angular speed is ωᵣₑₗ=ωₛₐₜ+ωₑ. Step 2: Seeing the satellite over the same equatorial location every 6 h means relative angular displacement 2π every 6 h, hence ωᵣₑₗ=2π/6=π/3 rad/h. Step 3: ωₛₐₜ=π/3−π/12=π/4 rad/h. Therefore n=4. (Source prints key 8, inconsistent with the stated 6 h and retrograde direction.)