A particle is projected vertically upwards from the surface of the earth (radius Rₑ) with a speed equal to one fourth of escape velocity. The maximum height attained by it from the surface of the earth is Rₑ/(5N). Then N is
Physics · Mixed Chapter
JEE Mains

Question

A particle is projected vertically upwards from the surface of the earth (radius Rₑ) with a speed equal to one fourth of escape velocity. The maximum height attained by it from the surface of the earth is Rₑ/(5N). Then N is

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Escape speed squared is vₑ²=2GM/Rₑ, so the launch speed satisfies u²=vₑ²/16=GM/(8Rₑ). Step 2: Apply energy conservation between the surface and the highest point rₘ: ½u²−GM/Rₑ=−GM/rₘ. Step 3: GM/(16Rₑ)−GM/Rₑ=−15GM/(16Rₑ), hence rₘ=16Rₑ/15. Step 4: Height above surface is h=rₘ−Rₑ=Rₑ/15=Rₑ/(5×3). Thus N=3.